Question

14) The difference of two squares is equal to 4,000 square cm. The edge of the smaller squareis 20 cm less than that of the larger square. Find the edge of the smaller square.

Answer 1

The edge of the smaller square = 90 square cm

Explanation:

Let the edge of the smaller square = x

let the edge of the larger square be y

`\begin{gathered} \text{difference of two squares is written as} \\ (x^2^{}-y^2)^{}\text{ = (x - y) (x + y)} \\ \text{Difference of two squares = 4000 cm}^2 \\ \text{mathematically} \\ (x^2-y^2)\text{ = 4000} \\ \text{note: the edge of the smaller square is 20 cm less than the edge of the larger square} \\ x\text{ = y - 20} \\ y\text{ = x + 20} \\ (x+20)^2-x^2\text{ = 400} \\ (x+20)(x+20)-x^2\text{ = 4000} \\ x^2+20x+20x+400-x^2\text{ = 4000} \\ \text{Collect the like terms} \\ x^2-x^2\text{ + 40x = 4000 - 400} \\ 40x\text{ = 3600} \\ \text{Isolate x} \\ (40x)/(40)\text{ = }(3600)/(40) \\ x=90cm^2 \\ \text{Hence, the edge of the smaller square is 90cm}^2 \end{gathered}`