The length of the hypotenuse of a 30°-60°-90° triangle is 12. what is the perimeter?

a. 6 + 18 √3
b. 36 + 12 √3
c. 12 + 36 √3
d. 18 + 6 √3

In a 30°-60°-90° triangle the hypotenuse (c) is twice the length of the shorter side (a):

So a = 12/2 = 6

The longer side (b) is equal to the shorter side multiplied by √3:

So b = 6√3

The three  side lengths are:

a = 6

b = 6√3

c = 12

The perimeter is the sum of the 3 sides:

Perimeter = 6 + 6√3 + 12 = 18 + 6√3

The answer is D.

what is the model?

step-by-step explanation:

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629