Question

The base of a triangle is nine centimeters longer than the perpendicular height. If the area of the triangle is 180 square centimeters, what is the length of the base, in centimeters?

Answer 1

The base is 24 cm long.

Explanation:

Equations

Let's call

b= base of the triangle

h=height of the triangle

The base is 9 cm longer than the height, thus:

b = h + 9

The area of the triangle is:

`\displaystyle A=(bh)/(2)`

`\displaystyle A=((h+9)h)/(2)`

And its value is 180:

`\displaystyle ((h+9)h)/(2)=180`

Multiplying by 2:

`(h+9)h=360`

Operating:

`h^2+9h-360=0`

Factoring:

`(h-15)(h+24)=0`

The only valid positive solution is:

h = 15 cm

And b = h + 9 = 24

b = 24 cm

The base is 24 cm long.