Question

please can someone help me, i can't work this question out!

Answer 1

Answer:

88 cm

Step-by-step explanation:

The area of a square = x², where x is the length of each side.

If the area of the square is 36 cm², then:

  36 = x²  

⇒  x = √36  

⇒  x = 6

So the length of each side of the square is 6 cm.  Therefore, the short side of the rectangle is 6 cm.

If the area of each rectangle is 1 and a third times the area of the square, then:

area = $1\frac{1}{3} \times36$

         = $\frac{4}{3} \times 36$

         = $\frac{4 \times36}{3}$

         = $\frac{144}{3}$

         = 48 cm²

So the area of each rectangle is 48 cm²

The area of a rectangle = width (W) x length (L)

We know the area of the rectangle, and that the width of the rectangle is equal to the side length of the square.  Therefore:

48 = 6 x L

L = 48/6 = 8

Therefore, the length of the rectangle is 8 cm.

Now we know the lengths of both sides of the rectangles, we can determine the perimeter.  From inspection of the diagram, there are 4 short sides and 8 long sides.  Therefore

Perimeter of shape = 4 x 6 + 8 x 8 = 24 + 64 = 88 cm