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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?

1 Answer

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The area of the original square patio will be 289 ft²

Step-by-step 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

User EmmanuelG
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