Find the leg of each isosceles right triangle when the hypotenuse is of the given measure. Given = 6 radical 2

Question

Find the leg of each isosceles right triangle when the hypotenuse is of the given measure.

Given = 6 radical 2

Answer 1

An isosceles right triangle is comprised of two EQUAL sides and a hypotenuse. The ratio of either side to the hypotenuse is 1:Square Root of 2 (radical 2). Therefore, whatever the length of the side (6), the hypotenuse is that length times the Square Root of 2 or Radical 2 - in this case 6 Radical 2. So the sides are both 6 (inches, centimeters...whatever the standard of measure). Conversely, if a hypotenuse is given as 6 radical 2, then the number preceding the radical 2 is the length of either side. Your answer is 6.

Answer 2

Hi John,

 

An isosceles right triangle will have angles of 45-45-90

 

There is a special relationship for all 45-45-90 triangles

 

The hypothenuse is equal to the leg time sgrt(2)

 

so

 

6sqrt(2) = leg * sqrt(2)

 

leg = 6

 

Hope this helps

Answer 3

let x=the measure of each leg

using the Pythagorean Theorem

x²+x²=(6√2)²

2x²=(36)(2)

divide both sides by 2

x²=36

√x²=√36

x=6 units for each of the legs