Algebra story problem

Question

the side of a square equals the width of a rectangle. the length of the rectangle is 10 meters longer than its width. the sum of the areas of a square and the rectangle is 100 sqaure meters. find the side of the square

Answer 1

Let L be the length of the rectangle.  Let s be the width of the rectangle as well as the side of the square.

 

L is also equal to 10 + s.

 

The sum of the areas of square and rectangle is 100.

 

Square:

 

A = s²

 

Rectangle:

 

A = Ls

 

L = 10 + s

 

 

Sum of areas:

 

Ls + s² = 100

 

Substitute for L.

 

(10 + s)s + s² = 100

 

Simplify.

 

10s + s² + s² = 100

 

2s² + 10s = 100

 

Put in standard form and attempt to factor.

 

2s² + 10s - 100 = 0

 

Divide all terms by two.

 

s² + 5s - 50 = 0

 

(s + 10)(s - 5) = 0

 

Algebraic solutions for s are negative 10 and 5, but since s is a length, it cannot be negative.

 

s = 5.