The longest side of an acute triangle measures 30 inches. the two remaining sides are congruent, but their length is unknown.

10 answers
Question:

The longest side of an acute triangle measures 30 inches. the two remaining sides are congruent, but their length is unknown.
what is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?
40.96 in.
51.22 in.
72.44 in.
81.22 in.

Answers

Really, we don't need to use that much math--we can use logic instead. Since the two congruent sides must be longer than 30in, the total has to be greater than 60in (the longest side plus the congruent sides.) So for our answer, we want the smallest total that is above sixty, which in this case is 72.44in.

Hope I helped, and let me know if you have any questions :) I can explain the real math if you want, it was just unnecessary here.

the answer is C guys lol

(C)72.4 in

Step-by-step explanation:

Given an acute triangle in which the longest side measures 30 inches; and the other two sides are congruent.

Consider the attached diagram

AB=BC=x

However to be able to solve for x, we form a right triangle with endpoints A and C.

Since the hypotenuse is always the longest side in a right triangle

Hypotenuse, AC=30 Inches

Using Pythagoras Theorem

[tex]30^2=x^2+x^2\\900=2x^2\\x^2=450\\x=\sqrt{450}\\x=21.21$ inches[/tex]

Therefore, the smallest possible perimeter of the triangle

Perimeter=2x+30

=2(21.21)+30

=42.42+30

=72.4 Inches (rounded to the nearest tenth)


[tex]The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but[/tex]

72.4 in.

Step-by-step explanation:

72.4 inch

Step-by-step explanation:

Length of the longest side = 30 inch

Let the length of two congruent side is x.

As the triangle is acute and the two sides are congruent, so it means it is an isosceles right angled triangle.

So, length of longest side is hypotenuse.

By use of Pythagoras theorem

[tex]hypotenuse^{2}=base^{2}+height^{2}[/tex]

[tex]30^{2}= x^{2}+x^{2}[/tex]

[tex]900^{2}=2x^{2}[/tex]

x = 21.2 inch

Perimeter = sum of all the sides

P = 30 + 21.2 + 21.2 = 72.4 inch

72.4

Step-by-step explanation: Because it is

Good evening ,

______

≈72,4

____________________

Step-by-step explanation:

Look at the photo below for the details.

:)


[tex]The longest side of an acute triangle measures 30 inches. the two remaining sides are congruent, but[/tex]

The answer is C. 72.44

The smallest possible perimeter of the triangle, rounded to the nearest tenth is 72.4 in

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Let

x > the length of  the remaining side

Applying the triangle inequality theorem

1) x+x > 30

2x > 30

x > 15 in

The perimeter is equal to

P=30+2x

Verify each case

1) For P=41.0 in

substitute in the formula of perimeter and solve for x

41.0=30+2x

2x=41.0-30

x=5.5 in

Is not a solution because the value of x must be greater than 15 inches

2) For P=51.2 in

substitute in the formula of perimeter and solve for x

51.2=30+2x

2x=51.2-30

x=10.6 in

Is not a solution because the value of x must be greater than 15 inches

3) For P=72.4 in

substitute in the formula of perimeter and solve for x

72.4=30+2x

2x=72.4-30

x=21.2 in

Could be a solution because the value of x is greater than 15 inches

4) For P=81.2 in

substitute in the formula of perimeter and solve for x

81.2=30+2x

2x=81.2-30

x=25.6 in

Could be a solution because the value of x is greater than 15 inches

therefore

The smallest possible perimeter of the triangle, rounded to the nearest tenth is 72.4 in

Are you doing Pythagory and theorem
 

Similar Solved Works

8 answers

I'm learning algebra and I need a better way of explaining it

I'm learning algebra and I need a better way of explaining it...
4 answers

What can lipids offer to us that that the other applicants cannot?

What can lipids offer to us that that the other applicants cannot?...
3 answers

The graph below represents which of the following functions?

The graph below represents which of the following functions? [tex]The graph below represents which of the following functions?[/tex]...
5 answers

What is the prepositional phrase in the sentence the minister from minnesota was the last speaker

What is the prepositional phrase in the sentence the minister from minnesota was the last speaker...
3 answers

How many players are allowed per team to be on the field at one time in flag football

How many players are allowed per team to be on the field at one time in flag football...
9 answers

There is a geometric theorem that says 'if two lines in a plane areperpendicular to the same line, they

There is a geometric theorem that says "if two lines in a plane areperpendicular to the same line, they are parallel to each other." explain why thisis true by writing and comparing equations for two different lines that areperpendicular to y=-1/3x hurry ! ​...
6 answers

Choose the correct formal command. aquí. venir venga vengas vens

Choose the correct formal command. aquí. venir venga vengas vens...
4 answers

Write (x^3)^5 using a single exponent

Write (x^3)^5 using a single exponent...
4 answers

Based on this map, which regions have the greatest concentration of poverty?

Based on this map, which regions have the greatest concentration of poverty?...
3 answers

PLS HELP I WILL GIVE BRAINLIESTWhere are we able to conduct research on Earth that can help us to learn more about and train for

PLS HELP I WILL GIVE BRAINLIEST Where are we able to conduct research on Earth that can help us to learn more about and train for a mission to Mars?...
3 answers

What does number 19 on the map represents

What does number 19 on the map represents...
4 answers

22. He_on his bicycle in going around the town? A . rides B. riding C. ride D. road​

22. He_on his bicycle in going around the town? A . rides B. riding C. ride D. road​ [tex]22. He_______on his bicycle in going around the town? A . rides B. riding C. ride D. road​[/tex]...
4 answers

Please can someone do this graph paragraph and without mistakes please it is necessary it should in ur own words

please can someone do this graph paragraph and without mistakes please it is necessary it should in ur own words [tex]please can someone do this graph paragraph and without mistakes please it is necessary it should in[/tex]...
4 answers

A rocket is launched from a tower. The height of the rocket, y in feet, is related to thetime after launch, x in seconds, by the

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y = -1622 + 1732 + 140...
1 answer

The following diagram shows two of the three orders of medieval society. use the diagram to answer the following question: an

The following diagram shows two of the three orders of medieval society. use the diagram to answer the following question: an illustration representing the positions of the church, the lords, and the peasants with the figure of jesus rising from the center. the lord and clergy members are huddled o...
6 answers

Find the whole.25% of what number is 60?Hi

Find the whole. 25% of what number is 60? Hi...
3 answers

What was significant about the law passing process within the 13 colonies during the articles of confederation?

What was significant about the law passing process within the 13 colonies during the articles of confederation?...
5 answers

What were the goals of the united states and russia in cold war?

What were the goals of the united states and russia in cold war?...
6 answers

Which of the following equations does not represent a proportional relationship?y=2xy is equal to 2 xy=12xy is equal to 1 half xy=3x+4y is equal to

Which of the following equations does not represent a proportional relationship? y=2xy is equal to 2 x y=12xy is equal to 1 half x y=3x+4y is equal to 3 x plus 4 y=0.3x...
3 answers

Mi-Young makes 24 cups of seafood kalguksu. This is 60% of the total kalguksu she makes.

Mi-Young makes 24 cups of seafood kalguksu. This is 60% of the total kalguksu she makes....

-- 0.044438--