Question

If the hypotenuse of an isosceles right triangle is 11√10, what is the length of each leg?

A) 11√2
B) 11√5
C) 11

Answer 1

B

Step-by-step explanation:

given the triangle is an isosceles right triangle

Then the legs are congruent (equal )

let each leg be x

using Pythagoras' identity in the right triangle

a² + b² = c²

a and b are the legs and c the hypotenuse

given hypotenuse = 11
`√(10)` , then

x² + x² = ( 11
`√(10)` )²

2x² = 1210 ( divide both sides by 2 )

x² = 605 ( take square root of both sides )

`√(x^2)` =
`√(605)` , that is

x =
`√(121(5))` =
`√(121)` ×
`√(5)` = 11
`√(5)`

Answer 2

The length of each leg of the isosceles right triangle is approximately √605 or 24.6.

Step-by-step explanation:

The length of the legs of an isosceles right triangle can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is given as 11√10. To find the length of each leg, we can set up the equation:

a^2 + b^2 = (11√10)^2

a^2 + b^2 = 1210

To simplify, we can write 1210 as 11^2 * 10:

a^2 + b^2 = (11^2 * √10^2)

a^2 + b^2 = (11^2 * 10)

Next, we can equate the squares of the legs:

a^2 = b^2

Substituting a = b, we get:

2a^2 = 1210

a^2 = 605

Therefore, the length of each leg is √605 or approximately 24.6. So the correct answer is not among the given options.