Rectangular stage.

Question

One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, what are the lengths of the sides

Answer 1

When a diagonal is drawn inside a rectangle, two congruent right triangles are formed.  The two legs of the right triangle are the two sides of the rectangle.

 

Let one side = x

Let the other side = x + 2

Diagonal = 10

 

Since we have a right triangle, we can use the Pythagorean theorem.

 

x² + (x + 2)² = 10²

 

x² + (x + 2)(x + 2) = 100

 

x² + x² + 4x + 4 = 100

 

2x² + 4x + 4 = 100

 

2x² + 4x - 96 = 0

 

 

Factor out a 2.

 

2(x² + 2x - 48) = 0

 

 

Set the term in parenthesis equal to zero.

 

x² + 2x - 48 = 0

 

(x - 6)(x + 8) = 0

 

x = 6           and          x = -8

 

 

Since we cannot have a negative dimension, we accept the positive value of x:

 

x = 6

 

 

Plug this value of x into the variables.

 

One side = 6 meters

The other side = 8 meters

 

 

6, 8, and 10 are Pythagorean triples.   This verifies we have a right triangle and the side lengths check out.