SOLUTION: A triangle is 10 inches wider than it is tall. If the area of the triangle is 28 square inches, what are the lengths of the height and the base?

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Question 948270: A triangle is 10 inches wider than it is tall. If the area of the triangle is 28 square inches, what are the lengths of the height and the base?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the length of the base be b and the length of the height h
the area of the triangle is: A=%281%2F2%29bh
given: A=28in%5E2 and
a triangle is 10 inches wider than it is tall; this means the length of the base b=h%2B10in

then,the area of the triangle is:
28=%281%2F2%29%28h%2B10%29h...solve for h
28=%28h%2F2%2B5%29h
28=h%5E2%2F2%2B5h
56=h%5E2%2B10h
0=h%5E2%2B10h-56
0=h%5E2-4h%2B14h-56
%28h%5E2-4h%29%2B%2814h-56%29=0
h%28h-4%29%2B14%28h-4%29=0
%28h%2B14%29%28h-4%29=0
solutions:
if %28h%2B14%29=0=> h=-14...disregard this solution because height cannot be negative
if %28h-4%29=0=> h=4
so, height is highlight%28h=4in%29, now find the length of the base
b=h%2B10in
b=4in%2B10in
highlight%28b=14in%29