Question

What are the dimensions of a right triangle with a ten-inch hypotenuse and an area of 25 square inches? (enter the lengths of the sides as a comma-separated list.)?

Answer 1

Let the legs of the triangle be x and y
using Pythagorean theorem:
c²=a²+b²
the hypotenuse will be:
x²+y²=10²
x²+y²=100
x²=100-y².......i
the area of the triangle is:
A=1/2bh
A=1/2xy
⇒25=1/2xy
50=xy
x=50/y
x²=2500/y²...ii
substituting ii in i and solving for y we get:
2500/y²=100-y²
2500=100y²-y^4

this can be written as:
y^4-100y^2+2500=0
thus 
y=5√2
x=50/(5√2)=5√2
thus:
Answer: (5√2,5√2)