Question

A square and a rectangle have the same area. The length of the rectangle is three inches more than the side of the square. The width of the rectangle is two inches less than the side of the square. Algebraically, find the dimensions of both the square and the rectangle.

Answer 1

Areas of rectangle , and square. Comparison and find its lengths

Area of rectangle = width x length = W x L

Area of square = (side length )^ 2

Length = (side length) + 3

Width = (side length ) -2

Then

(width x length ) = (side length)^2

W x L = S^2

Now replace W and L

(S + 3 )• ( S - 2) = S^2

this is a second degree equation

evelopeD

Eliminate parenthesis

S^2 - 2S + 3S - 6 = S^2

eliminate S^2

-2S + 3S -6 = 0

S - 6 = 0

Then

S = 6. Its side length of square

Then areacofnsq