Question

A parallelogram and a rhombus are equal in area. The diagonals of the rhombus measure 120 m and 44 m. If one of the sides of the ||gm is 66 m long, find its corresponding altitude.

Answer 1

Given: A parallelogram and a rhombus have equal area; the rhombus diagonals are 120 m and 44 m; one side (base) of the parallelogram is 66 m.

Step-wise calculation:

1. Area of the rhombus = `1/2 × "product of diagonals"` 

= `1/2 xx 120 xx 44` 

= 60 × 44

= 2640 m²

2. Since the parallelogram has the same area, its corresponding altitude h satisfies:

base × h = area

⇒ 66 × h = 2640

3. Solve for h:

h = 2640 ÷ 66

= 40 m

The corresponding altitude of the parallelogram is 40 m.