SOLUTION: please help me with this following polynomial equation word problem and please show work so i know and understand how to do it. The area of a right triangle is 250 in^2. Find t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help me with this following polynomial equation word problem and please show work so i know and understand how to do it. The area of a right triangle is 250 in^2. Find t      Log On


   



Question 90350This question is from textbook algebra and trigonometry
: please help me with this following polynomial equation word problem and please show work so i know and understand how to do it.
The area of a right triangle is 250 in^2. Find the lengths of its leg if one of the leg is 5 inches longer then the other. (use the five step method.)
This question is from textbook algebra and trigonometry

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the length of the legs of a right triangle if the area is 250 sq.in. and one leg is 5" more than the other leg.
Starting with the formula for the area of a triangle: A+=+bh%2F2
A = 250 sq.in.
let b = x, then h = x+5, so...
250+=+x%28x%2B5%29%2F2 Multiply both sides by 2.
500+=+x%28x%2B5%29 Perform the indicated multiplication on the right side.
500+=+x%5E2%2B5x Put this into the standard form for quadratic equations (ax%5E2%2Bbx%2Bc+=+0) by subtracting 500 from both sides.
x%5E2%2B5x-500+=+0 Factor this trinomial.
%28x%2B25%29%28x-20%29+=+0 Apply the zero products principle.
x%2B25+=+0 or x-20+=+0
x+=+-25 or x+=+20 Discard the negative solution as side lengths are positive.
x+=+20inches, and...
x%2B5+=+25inches.
The legs are: 20 inches and 25 inches.
Check:
A+=+%2820%29%2825%29%2F2
A+=+500%2F2
A+=+250sq.in.