SOLUTION: Base of a triangle is 7cm greater than the height. The area is 22cm². Find the height and length of the base. Height____ base _____.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Base of a triangle is 7cm greater than the height. The area is 22cm². Find the height and length of the base. Height____ base _____.       Log On


   

Question 162999: Base of a triangle is 7cm greater than the height. The area is 22cm². Find the height and length of the base. Height____ base _____.

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

Remember: Area%5BT%5D=%281%2F2%29bh --------------> working eqn
But as per condition, b=h%2B7cm
So,
A%5BT%5D=%281%2F2%29%28h%2B7%29%28h%29
22cm%5E2=%281%2F2%29%28h%5E2%2B7h%29, cross multiply & transpose
22%2A2=h%5E2%2B7h
h%5E2%2B7h-44=0
factor out being a perfect square:
%28h%2B11%29%28h-4%29=0
h=-11, No good
highlight%28h=4cm%29 ANSWER
so, highlight%28b=4%2B7=11cm%29
Check via working eqn,
22cm%5E2=%281%2F2%29%2811%29%284%29
22cm%5E2=%281%2Fcross%282%29%29%28cross%2844%2922%29
22cm%5E2=22cm%5E2
Thank you,
Jojo