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If two opposite sides of a square are increased by 14 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 72 square meters. find the area of the original square.

Respuesta :

barnuts

Let us call that the original side of the square is called “s”.

So the new dimensions are:

(s – 14) and (s – 7)

 

The formula for area of rectangle is:

A = l * w

 

therefore:

72 = (s – 14) * (s – 7)

s^2 – 7s – 14s + 98 = 72

s^2 – 21s = -26

Completing the square:

s^2 – 21s + 110.25 = -26 + 110.25

(s – 10.5)^2 = 84.25

s = 10.5 ± 9.18

s = 1.32, 19.68

 

s must be bigger than 14, so the correct side of the square is:

s = 19.68 m

 

So the area of the original square is:

A = s^2 = (19.68 m)^2

A = 387.3 square meters