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:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

Step-by-step 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:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}$

$x = \frac{-(-22)\±\sqrt{968}}{2*1}$

$x = \frac{22\±31.11}{2}$

Split

$x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}$

$x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}$

x can not be negative.

So:

$x = \frac{53.11}{2}$

$x = 26.56$

Recall that:

$y = 11 + x$

$y = 11 + 26.56$

$y = 37.56$

Hence, the dimensions are:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$