SOLUTION: The perimeter of a right triangle is 144 cm. The base is 12 cm. less than the width. Find the area.

Algebra ->  Systems-of-equations -> SOLUTION: The perimeter of a right triangle is 144 cm. The base is 12 cm. less than the width. Find the area.      Log On


   

Question 1108259: The perimeter of a right triangle is 144 cm. The base is 12 cm. less than the width. Find the area.
Found 2 solutions by ikleyn, rapaljer:
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
The perimeter of a right triangle is 144 cm. The base is 12 cm. less than the width. Find the area.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


The term "width" is NOT APPLICABLE to triangles.



Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = width
x-12 = base
c= hypotenuse
Perimeter = x + x-12 + c = 144
2x+c -12 = 144
2x+c= 156
c=156-2x

Since it's a right triangle, a%5E2+%2B+b%5E2+=+c%5E2
x%5E2+%2B+%28x-12%29%5E2+=+%28156-2x%29%5E2
+x%5E2+%2B+x%5E2-24x+%2B+144+=+156%5E2+-+624x+%2B+4x%5E2+
2x%5E2+-24x+%2B144=+24336+-624x%2B4x%5E2

0=+2x%5E2-600x+%2B+24192
0=+x%5E2+-300x+%2B+12096

Rewrite this to solve by completing the square
x%5E2+-300+%2B+____=-12096+%2B+______
x%5E2+-+300+%2B+22500+=+-12096+%2B+22500

+%28x-150%29+%5E2+=+10404

Take square root of both sides:
x-150=0+%2B-102
x=150+%2B-102
x=252 or x=48

The first answer is an extraneous root and must be rejected since the perimeter exceeds 144. The second answer gives legs of a right triangle to be 48 and 36, so the area is A=+1%2F2+%2A48%2A36+=+864+cm%5E2

Dr. Robert J. Rapalje, Retired
Email: rapaljer@mathinlivingcolor.com

For more FREE help with math, please see my website at www.mathinlivingcolor.com