SOLUTION: will you please help me with this word problem. The area of a right triangle is 250in2.find the lengths of its legs if one leg is 5 inches longer than the other.

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Question 24078: will you please help me with this word problem. The area of a right triangle is 250in2.find the lengths of its legs if one leg is 5 inches longer than the other.
Found 2 solutions by Paul, josmiceli:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
length No. 2= 5+x
Length no.1 = x

area of right triangle = 1%2F2+x+lw
250+=+x%285%2Bx%29%2F2
250+=+x%5E2%2B5x%2F2
250%282%29=x%5E2%2B5x
500=x%5E2%2B5x
x%5E2%2B5x-500=0
Use quadratic Forumla: x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in ax%5E2%2Bbx%2Bc a= 1, b = 5 and c=-500

x+=-5+%2B-+sqrt%28%285%292-4%281%29%28-500%29%29%2F+2%2A1%29
x=-5%2B-sqrt%2825%2B2000%29%29%2F+2%29
x=-5%2B-sqrt%282025%29%29%2F+2%29
Add:
x=-5%2B45%2F%282%29
x=20
20+5=25
And 20+x+25%2F%282%29
=250

Hence the one side of the right triangle is 20cm and the other side is 25 cm.
Paul.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for area is:
A+=+%281%2F2%29%2Ab%2Ah where b = base and h = height
Let the shorter leg = b
Then the longer leg = h = b + 5
250+=+%281%2F2%29%2Ab%2A%28b%2B5%29
250+=+%281%2F2%29%2Ab%5E2%2B%281%2F2%295%2Ab
b%5E2+%2B+5%2Ab+-+500+=+0
%28b+-+20%29%28b+%2B+25%29+=+0
this is true if b =20 or if b = -25
if b = 20, then h =25
then solve for A
A = 250