Question:
A parallelogram and a rhombus are equal in area. The diagonals of the rhombus measure 120 m add 44 m. If one of the sides of the ∥gm is 66 m long, find its corresponding altitude.
Solution:
Area of the rhombus $=\frac{1}{2}$ (Product of diagonals) $=\frac{1}{2}(120 \times 44)=2640 \mathrm{~m}^{2}$
Area of the parallelogram $=$ Base $\times$ Height $=66 \times$ Height
Given:
The area of the rhombus is equal to the area of the parallelogram.
Thus, we have:
$66 \times$ Height $=2640$
$\Rightarrow$ Height $=\frac{2640}{66}=40 \mathrm{~m}$
∴ Corresponding height of the parallelogram = 40 m
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