Question

(15 points)

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the leg of each isosceles right triangle when the hypotenuse is of the given measure.

Given = 5√6

Answer 1

Hi :) if you're coming from heritage and/or your answer needs a 2 in it, it would be 6 sqrt 2

Explanation:

Answer 2

Each of the legs of isosceles right triangle is 5
`√(3)`

Explanation:

Watch the attached figure for the isosceles right angled triangle

Looking at the figure we see that AB=5√6 and BC=CA

According to the Pythagorean theorem the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle.

1) Applying the Pythagorean theorem to the isosceles right triangle, we have

`BC^(2) + CA^(2) = AB^(2)`

2) Let BC=a and CA=a as they both are equal

So,

`a^(2) + a^(2) = (5√(6) )^(2)`

=>
`2a^(2) = (5√(6) )(5√(6) )`

=>
`2a^(2) = 5*5*√(6)*√(6)`

=>
`2a^(2) = 25*6` (since √6*√6 = (√6)²= 6)

=>
`2a^(2) = 150`

3) Dividing both sides by 2, we get

`(2a^(2) )/(2) =(150)/(2)`

4) Cancelling out the 2's on the left, we get

`a^(2)` = 75

5) Taking the square root on both sides, we have

`\sqrt{a^(2)} = √(75)`

=> a = 5
`√(3)`

So,

Each of the legs of isosceles right triangle is 5
`√(3)`