The height of a triangle is 1in. more than the base. If the height is increased by 2 in. while the base remains the same, the new area is becomes 20 in.^2

Question

Find the base and height of the original triangle. Find the area of the original triangle.

Answer 1

Hi Shay,

 

The area of a triangle is

S = b*h/2 where S is area, b is base and h is height.

 

if we let b=x, then h=x+1

if we increase h by 2 inches, the new h=(x+1)+2=x+3

 

S = x*(x+3)/2 = 20

(x²+3x)/2=20

(x²+3x)=40 (multiplied both sides by 2)

x²+3x-40 = 0 (subtracted 40 from both sides)

factorize and we get

(x+8)(x-5)=0

the roots are

x={-8,5}

we can't have negative length so the valid root is 5, which is equal to the length of the base.

Remember that h=b+1, so h=5+1=6

Then the area of the original triangle is 5*6/2=15 in²