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

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

→ 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=20 in2

Learning With Math

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