Question

If A is a square and B,C and D are all rectangles, find the dimensions of all rectangle D. The areas of the rectangles appear inside each one.

Answer 1

Step 1:

$\begin{gathered} \text{Area of a square A = 144 cm}^2 \\ \text{Length of it side L = }\sqrt[]{144} \\ L\text{ = 12 cm} \end{gathered}$

Step 2:

$\begin{gathered} \text{Area of B = }192cm^2 \\ \text{Length = L} \\ \text{Bread = 12} \\ Since\text{ B is a rectangle.} \\ \text{Area of B = L x B} \\ 192\text{ = }12L \\ L\text{ = }\frac{192}{12}\text{ = 16 cm} \end{gathered}$

Step 3:

Length of rectangle C = 16 + 12 = 28 cm

Breadth = B

Area of rectangle C = L x B

168 = 28B

$B\text{ = }\frac{168}{28}\text{ = 6cm}$

Step 4:

Area of D = 108

Breadth B = 12 + 6 = 18 cm

Length = L

Area of D = L x B

108 = 18L

$\begin{gathered} L\text{ = }\frac{108}{18} \\ L\text{ = 6 cm} \end{gathered}$

Final answer

The dimensions of rectangle D is 18cm by 6cm