a garden is designed in the shape of a rhombus formed from 4 identical 30° - 60° - 90° triangles. the…

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. what is the distance around the perimeter of the garden? 60 ft 60√3 ft 120 ft 120√3 ft

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. what is the distance around the perimeter of the garden? 60 ft 60√3 ft 120 ft 120√3 ft

Answer

Answer:

C. 120 ft

Explanation:

Step1: Analyze the 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the shorter leg (opposite 30°) is $x$, the hypotenuse is $2x$. Here the shorter leg of each 30 - 60 - 90 triangle is 15 ft (half of the 30 - ft shorter distance across the middle of the rhombus).

Step2: Find the side - length of the rhombus

Since the hypotenuse of each 30 - 60 - 90 triangle forms the side of the rhombus, and with $x = 15$ ft, the side - length $s$ of the rhombus is $s=2\times15 = 30$ ft.

Step3: Calculate the perimeter of the rhombus

The perimeter $P$ of a rhombus is given by $P = 4s$. Substituting $s = 30$ ft, we get $P=4\times30=120$ ft.