A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the mi
ddle of the garden measures 30 feet
60 ft
60 sq rt 3 ft
120 ft
120 sq rt 3 ft
2 answers:
Answer:
In Δ AOB, Right angled at O
So, side of rhombus = 30 cm
AO=15√3 cm
Length of another diagonal= 25.98 + 25.98= 51.96 cm, Because diagonals of rhombus bisect each other.
Area of Rhombus
=450√3 cm²
legs of the triangles
Each triangle 30-60-90 is:
one leg: 15 ft => short diagonal = 2 * 15ft = 30ft
other leg, x:
tan(30) = 15 / x => x = 15 ft / tan(30) = 25.98 ft
=> long diagonal = 2 * 25.98ft = 51.96 ft
side of the rhoumbus = hypotenuse of one triangle
side of the rhombus = √ [ (15)^2 + (25.98)^2 ] = √(900) = 30 ft
Area of the rhombus:
4 * area of one triangle = 4 [base*height/2] = 4*15*25.98/2 = 779.43 ft^2
The shortest distance accross the garden is equal to the side of the rhombus = 30 ft
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