A rectangular garden must have a perimeter of 155 feet and an area of at least 1400 square feet. Describe the possible lengths

10 answers
Question:

A rectangular garden must have a perimeter of 155 feet and an area of at least 1400 square feet. Describe the possible lengths of the garden. Round your answers to the nearest foot. The approximate length of the garden is at least feet and at most feet.

Answers

Step-by-step explanation:

Perimeter of a garden =  2(L+W)

Area of the gerden = LW

L is the length

W is the width

Given

Perimeter = 155ft

Area = 1400ft²

Substitute

1400 = LW

155 = 2L+2W

from 1;

W = 1400/L

Substitute into 2;

155 = 2L + 2(1400/L)

155 = 2L + 2800/L

155L = 2L² + 2800

2L²-155L + 2800 = 0

Factorize

L = 155±√155²-4(2)(2800)/4

L = 155±√24025-22400/4

L = 155±√1625/4

L = L = 155±40.31/4

L = 194.31/4

L = 48.82 feet and;

L = 155-40.31/4

L = 28.67ft

Hence the approximate length of the garden is at least 28.67 feet and at most 48.82 feet.

(3.14)x (4000)2
3.14 ) X (8000

Is 25,120

480 m - hope this helps

40

Step-by-step explanation:

20 times 20 is 400 20 plus 20 is 40

468.4 meters

Step-by-step explanation:

Find the width of the rectangle.

The area of a rectangle is A=length*width. Substitute the values of length and area and solve for width.

A=length*width

8,400=140*width

60= width

Use the width of the rectangle to find the circumference of the semicircles. Since each semicircle is half of a​ circle, the perimeter of the two semicircles is equal to the circumference of one circle.

The circumference of a circle is equal to pi​d, where d is the diameter. The diameter of the semicircle is the same as  the width of the rectangle.

​So, the diameter is 60 meters. Substitute the diameter into the formula for the circumference and simplify using 3.14 for pi.

≈188.4

(2 times 140)+ 188.4

​So, the perimeter of the track is 468.4 meters.

468.4 meters

Step-by-step explanation:

Find the width of the rectangle.

The area of a rectangle is A=length*width. Substitute the values of length and area and solve for width.

A=length*width

8,400=140*width

60= width

Use the width of the rectangle to find the circumference of the semicircles. Since each semicircle is half of a​ circle, the perimeter of the two semicircles is equal to the circumference of one circle.

The circumference of a circle is equal to pi​d, where d is the diameter. The diameter of the semicircle is the same as the width of the rectangle.

​So, the diameter is 60 meters. Substitute the diameter into the formula for the circumference and simplify using 3.14 for pi.

≈188.4

(2 times 140)+ 188.4

​So, the perimeter of the track is 468.4 meters.

Concept:

(i) In general, the length of any rectangle is always greater than its width.

(ii) Area of rectangle (A) = L × B

(iii) Perimeter of rectangle (P) = 2 ( L + B)

Given: Area of rectangle 'A' = 400 square meters

Let 'L' and 'B' be the length and width of the given rectangle.

According to the problem,

L = 3 B - 23 ------------------(1)

Area of the rectangle = 400 m²

or, L× B = 400 m²

or, (3 B - 23 )×B = 400

or, 3 B² - 23 B - 400 = 0

Apply, discriminant method,

Here, we will calculate only the positive value of B because width or length will never be negative.

[tex]B = \frac{23 +\sqrt{23^{2}+(4)(3)(400)}}{2(3)}\\ B = 16[/tex]

Now, using equation (1),

L = 3 B -23 = 3×16 - 23 = 25 m

Hence, length (L) = 25 m and Width (B) = 16 m

Now, we shall calculate the perimeter (P) of the rectangle

P = 2( L + B)

or, P = 2 (25 + 16 ) m

or, P = 82 m

Hence, the required perimeter of the given rectangle will be 82 m

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If it is a square then find the square root of 400. Which would get you 20. So 20 is the length of one side since it is a square you multiply 20 by 4 to get 80. The perimeter is 80 feet

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