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

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(52781) (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) (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,

Rewrite this to solve by completing the square

Take square root of both sides:

or

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

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

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

RELATED QUESTIONS
The perimeter of a right triangle is 144 cm. The base is 12 cm. less than the adjacent.... (answered by KMST,ikleyn)
The perimeter of an isosceles triangle is 36 cm and the area is 60 cm squared. The... (answered by ewatrrr)
The height of a right triangle is 5 cm more than its base. The area of the triangle is 42 (answered by Fombitz)
the height of a right triangle is 3 more cm than the base. if the area is 44 cm squared,... (answered by Big Poop)
2. The length of the hypotenuse of a right triangle is 13 cm. The length of one leg is... (answered by jim_thompson5910)
the width of a triangle is 15 cm less than the width. the perimeter is 98 cm. find the... (answered by rfer)
an equilateral triangle and a rectangle have the same perimeter. the length of a... (answered by addingup,ikleyn,MathTherapy)
The area of a base is 144 square centimeters. The height is 12 cm. Find the... (answered by Alan3354)
the base of a isosceles triangle is 12 cm and its perimeter is 32 cm.find the area of... (answered by lwsshak3)