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

###### Question:

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