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

D

Step-by-step 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 =

The answer is D.

Hope this helps!

Last one: 3√2

Step-by-step 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)

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.