Question

The length of the hypotenuse of a right triangle is three times the length of the shorter leg. The length of the longer leg is 12. What is the length of the shorter leg. Question 12 options: 2√3, √14.4, 6√2, 3√2

Answer 1

Last one: 3√2

Explanation:

Let the shorter length be S

Then,

The hypotenuse would be: 3S

Using pythagoras theorem,

(3S)² = S² + 12²

9S² = S² + 144

8S² = 144

S² = 18

S = sqrt(18)

S = 3sqrt(2)

Answer 2

D

Explanation:

Say the short leg is x and the hypotenuse is y. Then, y = 3x (because "The length of the hypotenuse of a right triangle is three times the length of the shorter leg.")

Use the Pythagorean Theorem: a^2 + b^2 = c^2 (where a and b are the legs and c is the hypotenuse). Here, we can say a = x and b = 12 and c = y. So:

x^2 + 12^2 = y^2

x^2 + 144 = (3x)^2

x^2 + 144 = 9x^2

8x^2 = 144

x^2 = 18

x =
`√(18) =3√(2)`

The answer is D.

Hope this helps!