Question

Each of the four shaded rectangles has an area of 21 cm square and a perimeter of 20cm what is the perimeter of the square formed in middle

Answer 1

16cm

Explanation:

Given

`Area = 21cm^2`

`Perimeter = 20cm`

`n=4` --- rectangles

Required

The perimeter of square in the middle

The area of a rectangle is:

`Area = L * W`

So, we have:

`L * W =21`

The perimeter is:

`P = 2*(L + W)`

So, we have:

`2*(L + W) = 20`

Divide by 2

`L + W = 10`

Make L the subject

`L = 10 - W`

Substitute
`L = 10 - W` in
`L * W =21`

`(10 - W) * W = 21`

Open bracket

`10W - W^2 = 21`

Rewrite as:

`W^2 -10W +21 = 0`

Expand

`W^2 -3W - 7W + 21 = 0`

Factorize

`W(W - 3) - 7(W - 3) = 0`

Factor out W - 3

`(W - 7)(W - 3) = 0`

Solve for 7

`W = 7\ W = 3`

We have:

`L = 10 - W`

This means that:

`W = 7\ W = 3`

`L = 3,\ L = 7`

The length (l) of the square is:

`l = |W - L|` ---- the difference between the dimension of the rectangle

`l = |7 - 3|`

`l = |4|`

`l = 4`

The perimeter is:

`P = 4l`

`P = 4*4`

`P =16`