# Area of a Triangle Word Problem

1. Feb 7, 2012

### S.R

1. The problem statement, all variables and given/known data
If the height of a triangle is five centimeters less than the length of its base and if the area of the triangle is 52 cm^2, find the base and the height.

2. Relevant equations
N/A

3. The attempt at a solution
height = h-5
base = h

A=(bh)/2

52=(h(h-5)/2

52=(h^2-5h)/2

104=h^2-5h

h^2-5h-104=0

(h-13)(h+8)=0

h=13 or h=-8

h=-8 is extraneous; therefore the base is 13 and the height is 8.

This is Grade 9 review and I don't think my teacher would include a problem using the quadratic equation. Is there an easier solution to this problem?

Last edited: Feb 7, 2012
2. Feb 7, 2012

### eumyang

There's always guess-and-check, I suppose...

I'm not sure why you don't think your teacher would include a problem using the quadratic equation. If we assume that Grade 9 = Algebra I (in the US), then sure, solving quadratic equations by factoring is an Algebra I topic.

3. Feb 7, 2012