Word problem

Question

The perimeter of a square and a rectangle are the same.The width of the rectangle is 6cm and its area is 16cm squared less than the area of the square. Find the area of the square.

Answer 1

The trick here is to be very careful reading the question and converting it into equations.

There are 2 unknowns: the length of the rectangle (call it x) and the side of the square (call it s).

The first sentence says 2(x+6) = 4s.

The next sentence says 6x = s² - 16.

 

From the linear equation s = (1/2)(x+6)

Substitute this into the other equation: 6x = (1/4)(x² + 12x + 36) - 16

Clear fractions and carefully collect terms: x² - 12 - 28

This factors as (x+2)(x-14)

The root x = -2 makes no physical sense.

The other root x = 14 solves the problem because from s = (1/2)(x+6), s = 10

 

Now check that the 2 perimeters are the same and that the relationship between the 2 areas is correct.