Question

The bricks are built to form a garden. The perimeter of the outer square is 264 centimeters. The area of the inner square is 900 square centimeters. What is the length and width of the brick.

Answer 1

The length and width is 44cm for the outer, 30cm for the inmer

Explanation:

For the outer square

264 centimeters is the perimeter, a square has four equal sides so the length and width will be the same

Formula for perimeter is ×+×+×+× =4×

So 4× =264

×=264÷4

×= 44

So one side is equal to 44cm and since all sides are equal length and width = 44cm

For the inner square

The area is equal to 900 square centimeters

The formula for area is length ×breath sine a square has equal sides

Length and breath is the same l×b

So

L×B = 900 square centimeters

The square root of 900 = 30

30×30= 900

So the answers is 30cm for the length and width of the square

Answer 2

Length: 124.7875 cm

Width: 7.2125 cm

Explanation:

The perimeter of this area can be calculated as:

P = 2L + 2W

Where P is the perimeter, L is the length and W is the width

If the perimeter is 264 centimeters, we have that:

2L + 2W = 264

L + W = 132

The area can be calculated as:

A = L*W

Where A is the area.

If the area is 900 cm2, we have that:

L*W = 900

From the first equation, we have that L = 132 - W

Using this value in the area equation, we have:

(132-W)*W = 900

132W - W2 = 900

W2 - 132W + 900 = 0

delta = b2 - 4ac = 17424 - 3600 = 13824

sqrt(delta) = 117.575

W1 = (132 + 117.575) / 2 = 124.7875 cm

W2 = (132 - 117.575) / 2 = 7.2125 cm

Using the smaller value for W, the length will be:

L + 7.2125 = 132

L = 124.7875 cm