the area of rhombus is equal to the area of triangle. if base of triangle is 24 cm, its corresponding altitude is 16 cm and one of the diagonals of the Rhombus is 19.2 cm. Find the it's another diagonal answer is 20 CM
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Answer:
Given
Base of the triangle,b = 24 cm
Altitude,h = 16 cm
Length of one diagonal, d₁ = 20 cm
Let the length of the other diagonal be d₂
Area of the triangle = 1
------ × b × h
2
1
= ------ × 24 × 16
2
= 192 cm²
∴ Area of the triangle = 192 cm²
Area of rhombus = 1
----- × d₁ × d₂
2
Area of the triangle = Area of the rhombus
192 = 1
----- × d₁ × d₂
2
192 = 1
----- × 20 × d₂
2
192 = 10 × d₂
d₂ = 192/ 10
d₂ = 19.2 cm cm
∴ Length of the other diagonal = 19.2