The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find the area of the rhombus.

Correct option is A

Given:

Perimeter of rhombus = 68 cm

One of the diagonal of rhombus = 16 cm

Formula used:

Perimeter of rhombus = $$2\sqrt{(\text{diagonal}_1)^2 + (\text{diagonal}_2)^2}$$​​

​Solution:​

​$$68 = 2\sqrt{(16)^2 + (\text{diagonal}_2)^2}\\\ \\4 = \sqrt{256 + (\text{diagonal}_2)^2}$$​​

Squaring on both sides

​$$1156 = 256 + (\text{diagonal}_2)^2\\\ \\1156 - 256 = (\text{diagonal}_2)^2\\\ \\900 = (\text{diagonal}_2)^2\\\ \\30 = \text{diagonal}_2$$​​

Area of rhombus = $$\frac{1}{2}$$​× diagonal 1 × diagonal 2

=  $$\frac{1}{2}$$​ × 16 × 30

=  16 × 15

= 240 sq cm