Question

Kelsey drew a rectangle with the same area as the square. The length of Kelsey's rectangle is 8 inches. What is the perimeter in inches of Kelsey's rectangle

Answer 1

perimeter of Keyley's rectangle is 20 inches.

Explanation:

Given : Keyle drew the rectangle 'R' and square 'S' with equal areas.The length of Kelsey's rectangle is 8 inches.

Find: What is the perimeter in inches of Kelsey's rectangle.

Solution:

Length of Keyley's rectangle = 8 inches.

Let the breadth be 'b' inches. Again, let 'l' be the length of a side of square .

Area of rectangle = area of square

length * width = length *length

8 * width =
`l^(2)`

Now, the only possible value of b is 2, so that

Area of square (
`l^(2)` )= 16

Plugging the values of
`l^(2)` = 16 in 8 * width =
`l^(2)`

8 * width =16

Width = 2

Perimeter of rectangle = 2 ( length + width)

Perimeter = 2 ( 8 + 2 )

Perimeter = 20 inches

Therefore, perimeter of Keyley's rectangle is 20 inches.

Answer 2

Answer: The answer is 20 inches.

Step-by-step explanation: As given in the question and shown in the attached figure, Keyley drew the rectangle 'R' and square 'S' with equal areas.

Also, the length of Keyley's rectangle 'R' = 8 inches. Let the breadth be 'b' inches. Again, let 'l' be the length of a side of square 'S'.

Then, we must have

`8* b=\ell^2.`

Now, the only possible value of b is 2, so that

`\ell^2=16\\\\\Rightarrow \ell=4.`

Thus, the breadth of 'R' is b = 2 inches and side of 'S' = 4 inches.

Therefore, perimeter of Keyley's rectangle 'R' is given by

`p=8+2+8+2=20~\textup{inches}.`

Thus, the answer is 20 inches.