The area of a triangle whose legs are in the ratio of 2:3 is 48. The length of the hypotenuse is

Question

a. square root 13
b. 8
c. 2 square root 52
d. 12
e. 208

please answer and explain

Answer 1

I assume it is a right triangle.

Area = 48 = 1/2 hb

96 = hb

Set one variable as multiple of 2 and see if the same multiple of 3 will multiply to = 96.

Pythagorean theorem:

8^2 + 12^2 = Hyp^2

64 + 144 = 208 = Hyp^2

√208 does not match any of your choices.
14 < √208 < 15.

Do you have any typos? Did you omit the square root symbol from the last choice?

Answer 2

that is my homewrok, i didn't omit the square root symbol from the last choice

Answer 3

e. 208

Answer 4

or, look at it as a scaling problem.

In a right triangle with legs 2 and 3, the hypotenuse is √13, and the area is (1/2)(2)(3) = 3.

Your triangle has a an of 48, which is 16*3

Since the area scales as the square of the scale factor, the hypotenuse is 4*√13 = 2√52

Answer 5

thank you