Question

The length of the hypotenuse of a 30 -60 -90 triangle is 16. What is the perimeter?

64+8 square root 3
24+8 square root 3
16+64 square root 3
8+24 square root 3

Answer 1

24+8 square root 3

I hope I helped

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Answer 2

Option B is correct

the perimeter is,
`24+8√(3)` units

Explanation:

Let H represents the Hypotenuse side, S represents the shorter side and L represents the side of the longer.

In a 30-60-90 triangle,

The hypotenuse is twice the length of the shorter leg,

and the length of the longer leg is
`√(3)` times the length of the shorter leg.

As per the statement:

The length of the hypotenuse of a 30 -60 -90 triangle is 16

⇒
`\text{Length of hypotenuse side} = 16` units.

then by definition of 30-60-90 triangle.

⇒
`H = 2S`

⇒
`16 = 2S`

⇒
`8 = S`

or

S = 8 units

Also. length of the longer leg is
`√(3)` times the length of the shorter leg

⇒
`L = √(3) \cdot 8`

⇒
`L = 8√(3)` units

Perimeter(P) of a 30-60-90 triangle is sum of all the three sides i.e,

`P = L+S+H = 8√(3)+8+16 = 8√(3)+24`

Therefore, the perimeter is,
`24+8√(3)` units