Question

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

A rhombus is shown. Lines are drawn from each point to the opposite point to form 4 right triangles. The other 2 angle measures are 30 and 60 degrees. The base length of each triangle is 15 feet.

What is the distance around the perimeter of the garden?

a 60 ft
b 60 StartRoot 3 EndRoot ft
c 120 ft
d 120 StartRoot 3 EndRoot ft

Answer 1

The shorter diagonal is 30 ft, so each right triangle formed by the diagonals has the short leg = 30/2 = 15 ft. In a 30°-60°-90° triangle the hypotenuse = 2 × short leg, so each side of the rhombus = 2·15 = 30 ft. Perimeter = 4·30 = 120 ft.

Answer: c. 120 ft.