Question

the perimeter and the length of one of the diagonals of a rhombus is 34cm and 8cm respectively find the length of its other diagonal​

Answer 1

The length of the other diagonal is 15 cm.

• The perimeter of the rhombus is given as 34 cm.

Sum of 4 sides = 34 cm

• Let the side of rhombus be x

4x = 34

x = 8.5 cm

• Length of each side of rhombus is 8.5 cm

• Area of rhombus is given by using one side and one diagonal is $\frac{1}{2}p(\sqrt{4a^2-p^2})$, where a is the side of rhombus and p is the diagonal of rhombus.

• Substituting in the formula we get,

A = $\frac{1}{2}8(\sqrt{4(8.5)^2-8^2})$

A = 4× 15 = 60 sq. cm

• Now to find the area of the other diagonal, we apply the formula,

Area = (1/2) × product of both the diagonals

60 = 8 × other diagonal ÷ 2

120 = 8 × other diagonal

other diagonal = 15

• Length of the other diagonal is 15 cm.