SOLUTION: The base of a triangle is 3cm longer than it's corresponding height. If the area is 44cm^2, find the length of it's base

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The base of a triangle is 3cm longer than it's corresponding height. If the area is 44cm^2, find the length of it's base       Log On


   

Question 927524: The base of a triangle is 3cm longer than it's corresponding height. If the area is 44cm^2, find the length of it's base

Found 2 solutions by MathLover1, ewatrrr:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
the base of a triangle a is 3cm longer than it's corresponding height h
the area is 44cm%5E2
A=a%2Ah%2F2
if a=h%2B3cm, then
44cm=%28h%2B3cm%29%2Ah%2F2
44cm%5E2%2A2=h%5E2%2B3hcm
88cm%5E2=h%5E2%2B3hcm
0=h%5E2%2B3hcm-88cm%5E2

h+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

h+=+%28-3cm+%2B-+sqrt%28+%283cm%29%5E2-4%2A1%2A%28-88cm%5E2%29+%29%29%2F%282%2A1%29+

h+=+%28-3cm+%2B-+sqrt%28+9cm%5E2%2B352cm%5E2%29+%29%2F2+

h+=+%28-3cm+%2B-+sqrt%28+361cm%5E2%29+%29%2F2+

h+=+%28-3cm+%2B-+19cm+%29%2F2+...we need only positive solution

h+=+%28-3cm+%2B+19cm+%29%2F2+

h+=+16cm+%2F2+

highlight%28h+=+8cm%29++

now, find the base:

a=h%2B3cm

a=16cm%2B3cm

highlight%28a=19cm%29=> the length of it's base



Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

.

A = (1/2)bh 

(1/2)(h+3)h = 44 cm^2

(h+3)h = 88

h^2 + 3h - 88 = 0  (tossing out negative solution for unit measure)

(h + 11)(h - 8)= 0

h = 8cm  and Base = 11cm 8%2B3

And ...checking

(1/2)(8cm)(11cm) = 44cm^2