SOLUTION: A triangle has an area of 10 cm2. The height of the triangle is 4 cm longer than three times the base. Find the height and base of the triangle.

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Question 659094: A triangle has an area of 10 cm2. The height of the triangle is 4 cm longer than three times the base. Find the height and base of the triangle.
Answer by nicy12(9) About Me  (Show Source):
You can put this solution on YOUR website!
"A triangle has an area of 10 cm2. The height of the triangle is 4 cm longer than three times the base. Find the height and base of the triangle."
A=10cm2
h=4+3b
find h and b

A=1/2(bh)
10cm2=[b(4+3b)]/2
20cm2=4b+3b2
3b2+4b-20=0
using quadratic equation:

a=3 ; b=4 ; c=-20
base=%28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
base=%28-4%2B-sqrt%284%5E2-4%2A3%2A-20%29%29%2F%282%2A3%29
base1=2
base2=-3.333

we will take base 1 because it is positive
h=4+3b
h=4+3(2)

h=10
checking:
A=1/2(bh)
A=1/2(2)(10)
10cm2=10cm2 (correct)
the base and height is 2cm and 10cm respectively.
i hope it helped you :)