Question

The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.​ (Hint: An isosceles right triangle is a right triangle whose legs are the same​ length.)

Answer 1

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

`Hypotenuse:37.56`

`Other\ Legs: 26.56`

Explanation:

Let the hypotenuse be y and the other legs be x.

So:

`y = 11 + x`

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

`y^2 = x^2 + x^2`

`y^2 = 2x^2`

This gives:

`(11+x)^2 = 2x^2`

Open bracket

`121 + 22x + x^2= 2x^2`

Collect like terms

`2x^2 - x^2 -22x - 121 = 0`

`x^2 -22x - 121 = 0`

Using quadratic formula:

`x = (-b\±√(b^2 - 4ac))/(2a)`

`x = (-(-22)\±√((-22)^2 - 4*1*-121))/(2*1)`

`x = (-(-22)\±√(968))/(2*1)`

`x = (22\±31.11)/(2)`

Split

`x = (22+31.11)/(2)\ or\ x = (22-31.11)/(2)\\`

`x = (53.11)/(2)\ or\ x = (-9.11)/(2)`

x can not be negative.

So:

`x = (53.11)/(2)`

`x = 26.56`

Recall that:

`y = 11 + x`

`y = 11 + 26.56`

`y = 37.56`

Hence, the dimensions are:

`Hypotenuse:37.56`

`Other\ Legs: 26.56`