Question

Terry had a square patio. After expanding the length by 20 ft and the width by 10 ft, the area was 999 ft2 . What was the original area?

Answer 1

The area of the original square patio will be 289 ft²

Explanation

Suppose, the side length of the original square patio is $x$ ft.

So, the area of the square patio will be: $x*x= x^2$ ft²

After expanding the length by 20 ft and the width by 10 ft, the new length will be: $(x+20)ft$ and the new width will be: $(x+10)ft$

As the formula for area is $(length*width)$ and the area is given as 999 ft² , so the equation will be......

$(x+20)(x+10)=999\\ \\ x^2+30x+200=999\\ \\ x^2 +30x+200-999=0\\ \\ x^2+30x-799=0\\ \\ (x-17)(x+47)=0$

Using zero-product property, we will get.....

$x-17=0\\ x=17\\ \\ and\\ \\ x+47=0\\ x= -47$

(Negative value of x is ignores as the side length can't be in negative)

So, the area of the original square patio will be: $x^2= (17)^2= 289 ft^2$