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.) ?

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)