The length of the hypotenuse of a 30°-60°-90° triangle is 7. Find the perimeter.
(1 point)
In a 30°-60°-90° triangle, the sides are in a ratio of 1:2:√3.
Let x be the length of the shorter leg.
Then the length of the longer leg is 2x.
The hypotenuse is √3x.
Given that √3x = 7, solve for x:
x = 7/√3 = 7√3/3
The length of the shorter leg is x = 7√3/3.
The length of the longer leg is 2x = 14√3/3.
The length of the hypotenuse is √3x = 7.
The perimeter is the sum of the lengths of the three sides:
Perimeter = x + 2x + √3x
= 7√3/3 + 14√3/3 + 7
= (7/3 + 14/3)√3 + 7
= 21/3√3 + 7
= 7√3 + 7.
Therefore, the perimeter of the triangle is 7√3 + 7.