Question

Please help.

The length of the hypotenuse of a 30 degree-60 degree-90 triangle is 25 what is the perimeter?

Answer 1

The perimeter = 59.15 units to the nearest hundredth.

Explanation:

The ratio of the sides in a 30/60/90 triangle are 1 : √3 : 2, so if the hypotenuse is 25 units long, then the shortest side = 1/2 * 25 = 12.5 and the other side, by proportion = 25*(√3 / 2) = 21.65 units.

Therefore the perimeter = 25 + 12.5 + 21.65 = 59.15 units (answer).

Answer 2

Since we have a 30° - 60° - 90° triangle, we can calculate any side by knowing at least one out of three:

Since the length of the hypotenuse is twice as long as the shorter leg, we have:

The length of the short leg is: 25/2 = 12.5

Since the length of the longer leg is equal to the length of the shorter leg

multiply by square root of 3 we have:

The length of the longer leg is: 12.5 × √3 ≈21.65

=> The perimeter of the triangle is: 25 + 12.5 + 21.65 = 59.15