Question

Find the length of the legs of a right triangle if both legs are equal and the hypotenuse is 10?

Answer 1

length of the legs is
`5√(2)`

Explanation:

the both sides of the length of the legs of a right triangle are equal

So it form a isosceles triangle 45- 45- 90 degree triangle

the ratio of 45-45-90 degree triangle is
`x:x:x√(2)`

xsqrt(2) is the side opposite to 90 degree

so
`hypotenuse =x√(2)`

`10=x√(2)`

Divide both sides by square root (2)

`(10)/(√(2))=x`

multiply square root (2) at the top and bottom

`(10 \cdot √(2))/(2)=x`

`x=5√(2)`

length of the legs is
`5√(2)`