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

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

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)