SOLUTION: Could some one please help I do not remember how to solve this kind of problem. The base of a triangle is 4cm greater then the height. the area is {{{48cm^2}}}Find the height and

Algebra ->  Triangles -> SOLUTION: Could some one please help I do not remember how to solve this kind of problem. The base of a triangle is 4cm greater then the height. the area is {{{48cm^2}}}Find the height and       Log On


   

Question 135418: Could some one please help I do not remember how to solve this kind of problem.
The base of a triangle is 4cm greater then the height. the area is 48cm%5E2Find the height and length of the base.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the area of a triangle:
A+=+%281%2F2%29bh where: b is the length of the base and h is the length of the height.
In your problem, you have b = h+4 (The base (b) is 4 cm greater than the height (h)) and:
A+=+48 (The area is 48 sq.cm.), so...
A+=+%281%2F2%29bh Substitute A = 48, and b = h+4.
48+=+%281%2F2%29%28h%2B4%29h Simplify and solve for h.
48+=+%281%2F2%29%28h%5E2%2B4h%29 Multiply both sides by 2.
96+=+h%5E2%2B4h Subtract 96 from both sdes.
h%5E2%2B4h-96+=+0 Solve by factoring.
%28h%2B12%29%28h-8%29+=+0 Apply the zero products rule.
h%2B12+=+0 or h-8+=+0, so...
h+=+-12 or h+=+8 Discard the negative solution as lengths are positive quantities.
h+=+8 The height is 8cm.
The base is:
b+=+h%2B4
b+=+12 The base is 12cm.