Question

The length of the hypotenuse of a 30°-60°-90° triangle is 7. Find the perimeter

Answer 1

Rules for a 30-60-90 right triangle:
hyp = 2 * short leg
Long leg = sqrt(3) * short leg
Given:
hyp = 7
7 = 2*short leg
divide both sides by 2
7/2 = short leg
long leg = sqrt(3) * short leg
long leg = sqrt(3) * (7/2)
long leg = 6.06
P= s1 + s2 + s3
P = 7 + 3.5 + 6.06
P = 16.56 units      (Decimal approximation)
P = 10.5 + 3.5sqrt(3) units       (Exact value)

Answer 2

The shortest leg  = 1/2 * 7 = 3.5
longest leg = 7 * sqrt 3 = 12.12

Perimeter = 7 + 3.5 + 12.12  =  22.62 to nearest hundredth