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.

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) (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

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 :)
RELATED QUESTIONS
A triangle has an area of 36 cm2 and a base of 9 cm. The height of the triangle is... (answered by algebrahouse.com)

The base of a triangle is 4 cm greater than the height. The area is 48 cm2. Find the... (answered by jojo14344)

The base length of a right triangle is 4 cm more than its height. The area is 30 cm2.... (answered by josgarithmetic)

A triangle with an area of 120 cm2 has a height of 10 cm. What is the triangle's base... (answered by nerdybill)

Find the area of a triangle with base 10 cm and corresponding height 4... (answered by rajagopalan)

The base and height of a triangle total 14 cm and the area is 20 cm2. Find the dimensions (answered by ikleyn)

The height of a triangle is 5 centimeters longer than three times its base. Find the base (answered by drj)

the height of a triangle is 10 centimeters more than its base. if the area of the... (answered by mananth)