The base of a triangle is 24cm and corresponding altitude is 16 cm. The area of a rhombus is equal to the area of the triangle . If one of the diagonals of the rhombus is 20 cm, find the length of the other diagonal.
Answers
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