How would i find the length? ?

Question

if the hypotenuse of a triangle is twice as long as one of its legs, and the other leg is 9 inches long, how would i find the hypotenuse?

Answer 1

Since we have the ratio of one leg to the hypotenuse, we can define the hypotenuse in terms of one of the legs.

Since c=2b, and a=9, we can say

9^2+b^2=(2b)^2

81+b^2=4b^2

81=3b^2

9=b sqrt(3)

b=9/sqrt(3)

b=9sqrt(3)/3

b=3sqrt(3)

2b=6sqrt(3)

2b=c

c=6sqrt(3) <===ANSWER

Answer 2

Since you have a hypotenuse, you're indicating it's a right triangle because a hypotenuse only exists on a right triangle.

Use Pythagorean theorem to solve.

a² + b² = c²

c = h = 2L

b = L (L = one of the legs)

a = 9

9² + (L)² = (2L)²

81 + L² = 4L²

81 = 3L²

27 = L²

L = √(27) = 3√3

H = 6√3

Answer 3

Usually, this theorem is expressed as a2+b2=c2.

The pythagorean theorem : the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.  

Answer 4

use A^2 + B^2 = C^2

C= B x 2

A = 9

b = ?

9^2 + B^2 = (B x 2) ^2

81 + B^2 = 4B^2

81 = 3B^2

27 = B^2

square root of 27 = B

B= 5.196152423

A^2 + B^2 = C^2

81 + 27 =C^2

C = 10.39230485