Square ABCD with unknown side length x has one side decreased by 11 inches and the other side by 10 inches. The area of the resulting rectangle AEFG is 56 square inches.

Question

Square ABCD with unknown side length x has one side decreased by 11 inches and the other side by 10 inches. The area of the resulting rectangle AEFG is 56 square inche’s

Answer 1

The sides of the resulting rectangle will be x-11 and x-10.

Area of this rectangle ; (x-11) * (x-10)= 56

First way:

when distributed; x²-21x +54=0

when factored; (x-18)(x-3) = 0

then x= 18 or x= 3

The answer can be only 18 since the side of original square cannot be negative, x must be greater than 11)

Second way: Since x-11 and x-10 are consecutive numbers, we just need to find the two factors of 56 that are consecutive.

Factors of 56;

1, 56

2, 28

7, 8

Knowing x-11 is smaller than x-10. Set the equation as x-11= 7. Then x=18