Question

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

Answer 1

Answer:

Option B is correct

the perimeter is, $24+8\sqrt{3}$ units

Step-by-step 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 $\sqrt{3}$ 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 $\sqrt{3}$ times the length of the shorter leg

⇒$L = \sqrt{3} \cdot 8$

⇒$L = 8\sqrt{3}$ units

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

$P = L+S+H = 8\sqrt{3}+8+16 = 8\sqrt{3}+24$

Therefore, the perimeter is, $24+8\sqrt{3}$ units

Answer 2

24+8 square root 3

I hope I helped

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