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

Answer:

16cm

Step-by-step 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:

$P = 4l$

$P = 4*4$

$P =16$