Question

The area of a right angle is 50. One of its angles is 45 degrees. Find the lengths of the sides and hypotenuse of the triangle.

Answer 1

It's isosceles triangle (look at the picture).

The area of the this triangle:
`A=(a^2)/(2)`

We have
`A=50`

Substitute:

`(a^2)/(2)=50\ \ \ |\cdot2\\\\a^2=100\to a=√(100)\to a=10`

Use the Pythagorean theorem:

`b^2=a^2+a^2\\\\b^2=100+100\\\\b^2=200\to b=√(200)\\\\b=√(100\cdot2)\\\\b=√(100)\cdot\sqrt2\\\\b=10\sqrt2`

Answer: 10, 10, 10√2