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True [87]
3 years ago
10

A triangle has a height that is 2 inches more than three times the base and an area of 60 in. Find the base and the height of th

e triangle.
Mathematics
1 answer:
const2013 [10]3 years ago
8 0

Answer:

Height = 20, Base = 6

Step-by-step explanation:

The area of a triangle is \frac{bh}{2}

where b is the base and h is the height

H = 3B + 2\\\frac{B(3B + 2)}{2}=60\\\\3B^2 + 2B = 120\\3B^2+2B - 120=0\\

We can factor by grouping

3B^2 - 18B + 20B - 120 = 0\\3B(B - 6) + 20(B-6) = 0\\GCF the (B-6)\\(B-6)(3B+20)=0\\B = 6, B = \frac{-20}{3}

Length can only be positive, so we know that the base is 6 in

The height must be 2 + 3(6) = 20

Height = 20, Base = 6

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