Question

Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.

Answer 1

Given: 
Side of the rhombus = 6 cm
Altitude = 4 cm 
One of the diagonals = 8 cm
Area of the rhombus = Side x Altitude \[= 6 x 4 = 24 {cm}^2 . . . . . . . . (i)\]
We know: Area of rhombus \[= \frac{1}{2} \times d_1 \times d_2 \]
Using (i): 
\[24 = \frac{1}{2} \times d_1 \times d_2 \]
\[24 = \frac{1}{2} \times 8 \times d_2 \]
\[ d_2 = 6 cm\]