The distance around the perimeter of the given garden in the shape of a rhombus is 120 ft.
What is a rhombus?
A parallelogram with all four sides equal and the diagonals intersecting at right angles is called a rhombus.
How do we solve the given question?
In the question, we are given that a garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. We are also informed that the shorter diagonal measures 30 ft.
We are asked to find the distance around the perimeter of the garden.
In the figure, we can see that AC is the shorter diagonal as it is opposite to the shorter angle, 60°, in comparison to BD, which is opposite to the larger angle, 120°.
We know that AC is bisected at O, as the four triangles are identical. Thus, we know that AO = 15 ft.
In ΔAOD,
sin 30° = AO/AD (perpendicular/hypotenuse)
or, 1/2 = 15/AD
or, AD = 15*2 = 30 ft.
Thus, AD = 30 ft.
As we know that in a rhombus, all sides are equal, and also the 4 triangles are identical, so we get AB = BC = CD = AD = 30ft.
We know the perimeter of a rhombus = 4a, where a is the length of the side of the rhombus.
Thus, Perimeter = 4*30 ft. = 120 ft.
∴ The distance around the perimeter of the given garden in the shape of a rhombus is 120 ft.
Learn more about a rhombus at
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