Unsure how to solve this word problem and how to get the answer.

Question

  A square and a triangle have the same area. The base of the triangle is 3 feet more than the side length of the square. The height of the triangle is 1 foot less than the base of the triangle. What is the side length of the square? What are the base and the height of the triangle? 

Answer 1

Let side of square = x

Let base of triangle = x + 3

Let height of triangle = x + 3 - 1 = x + 2

 

 

Now we use the variables to write the area equality.

 

x² = (x + 3)(x + 2) / 2

 

 

Solving for x,

 

x² = (x² + 5x + 6) / 2

 

 

Multiply both sides of the equation by 2.

 

2x² = x² + 5x + 6

 

 

Move all terms to the left side of the equation.

 

x² - 5x - 6 = 0

 

 

Factor the left side.

 

(x - 6)(x + 1) = 0

 

 

Setting the factors equal to zero gives you     x = 6     and     x = -1

 

 

Since we cannot have a negative value for length, we accept the positive value:   x = 6

 

Substitute this value of x into the variables to find the actual lengths.