Question

1. The area of a rectangle is 12 and the width is 3/4 the length. What are the dimensions?

2. One leg of a right triangle is 2 1/2 times the other and the area is 20. What are the dimensions?

Answer 1

1.
let x = the length
let (3/4) x = the width

The area of a rectangle = width * height.

area = width*height

12 = x*(3/4)x
12 = (3/4)x^2
12/(3/4) = x^2
16 = x^2
x=4. The answer x=-4 does not make sense in the context of the problem.

2.
let x = leg one
let 2.5x = leg two

The area of a triangle = base*height/2

area = base*height/2

20 = 2.5x*x/2
20 = 2.5x^2/2
20/2.5 = x^2/2
8 = x^2/2
16 = x^2
x=4. Again, the answer x=-4 does not make sense in the context of the problem.