The area of a rectangle with sides of 6 cm and 10 cm is equal to the area of a rhombus

The area of a rectangle with sides of 6 cm and 10 cm is equal to the area of a rhombus with a perimeter of 48 cm. Find the height of the rhombus.

1. S, P, h, c – area, perimeter, height, side of the rhombus, respectively, and and b – sides of the rectangle.

2. Calculate S of the rectangle:

S = a x h = 6 x 10 = 60 cm².

3. By the condition of the problem, the areas of both geometric figures are equal. Therefore, the rhombus also has an area of 60 centimeters².

4. We calculate the length of the side of the rhombus (c), taking into account that all its sides are equal:

s = P: 4 = 48: 4 = 12 cm.

5. S rhombus = s x h = 60 cm².

h = 60: 12 = 5 cm.

Answer: h equals 5 centimeters.