 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
Question from steven, a student: the perimeter of a right triangle is 20 cm. its area is 15 sq cm. find its hypotenuse. |
Steven,
Let the legs of the triangle have lengths x and y cm and the hypotenuse have length h cm.
The perimeter is 20 cm
x + y + h = 20.
The area is 15 sq cm
xy/2 = 15.
Hypotenuse tell us that
x2 + y2 = h2.
Hence
y = 30/x and h = Sqrt(x2 + y2) = Sqrt(x2 + (30/x)2)
Substitution into the first equation gives
Sqrt(x4 + 900) = 20x - x2 - 30.
Square both sides and simplify. The resulting equation is a quadratic which you can factor to find x.
Penny
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.