SOLUTION: The area of a right-angled triangle is 48cm(squared). The base of the triangle is 4cm more than the height. Find the base and height of the triangle. I get confused with this quest

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Question 401669: The area of a right-angled triangle is 48cm(squared). The base of the triangle is 4cm more than the height. Find the base and height of the triangle. I get confused with this question I know the answers from answer book and trial and error. I try to form into an quadratic equation like : h(h+4)=48cm(squared) but get confused plz help.
Found 2 solutions by edjones, Earlsdon:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
1/2 * bh=A
b=h+4
1/2 * h(h+4)=48
1/2(h^2+4h)=48
h^2+4h=96
h^2+4h-96=0
(h-8)(h+12)=0
h=8, b=12
.
Ed

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%29b%2Ah and the area is given a 48 sq.cm., so...
%281%2F2%29b%2Ah+=+48 but b = h+4, so substitute for b...
%281%2F2%29%28h%2B4%29%2Ah+=+48 Multiply both sides by 2.
%28h%2B4%29%2Ah+=+96 which becomes...
h%5E2%2B4h-96+=+0 So there's the quadratic in h. Solve by factoring.
%28h-8%29%28h%2B12%29+=+0
h+=+8 or h+=+-12 Discard the negative solution.
The height is 8cm. and the base is h+4 = 12cm.