The sides of a triangular park are 96m, 110m and 146m. Its area is equal to the area of a field in the shape of a rhombus, one of whose diagonals is 60m. the length (in m) of its other diagonal is:
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Correct answer: A
Explanation
The correct answer is Option 1 i.e. 176.
The sides of a triangular park are 96 m. 110 m and 146 m.
Its area is equal to the area of a field in the shape of a rhombus, one of whose diagonals is 60 m.
Semi perimeter of a triangle, S = (A + B + C)/2 (A, B, C is the length of three sides of the triangle)
Area of a triangle = √S(S - A)(S - B)(S - C)
S = Semi-perimeter of the triangle and A, B, C is the length of three sides of the triangle.
Area of a rhombus = Product of the length of the two diagonals ÷ 2
Semi perimeter of the triangular park = (96 + 110 + 146)/2 = 352/2 = 176 m
Area of the triangular park = √176(176 - 96)(176 - 110)(176 - 146) = √176(80)(66)(30) = √27878400 = 5280 m2
Let the length of the other diagonal of the rhombus be x m.
According to the concept -
(60 × x)/2 = 5280
x = (5280 × 2)/60
x = 176