Question

The height of a triangle is 4 feet less than the length of its base, b. The area of the triangle is 30 square feet.

Find the base and the height of the triangle.

Answer 1

Explanation:

h=b-4

A=30ft^2

A=1/2bh

30=1/2b(b-h)

Cross Multiply

60=b(b-4)

60=b^2-4b

b^2-4b-60=0

Factorise the equation

(b^2+6) (-10b-60)

b(b+6)-10(b+6)

(b-10) (b+6)

b-10=0 or b+6=0

b=10 or b=-6

base =10 (since measurement can not be negative)

h=b-4

Sub the value of b

h = 10-4

h=6

So the height is 6ft and base is 10ft