Question

The base of a triangle is 5 units greater than the height, if its area is 18cm2, what is the quadratic equation that models the situation described and is used to find the height of the triangle?

Answer 1

base= 5+h

height= h

area= 1/2bh, so since our area us 18cm^2

therefore 18=1/2*b*h

18*2=(5+h)*h

36=5h+h^2

h^2+5h-36=0 ( for quadratic equation)

h^2+9h-4h-36=0

(h^2+9h)(-4h-36)=0

h(h+9)-4(h+9)=0

(h-4)(h+9)=0

h=4 or h= -9