Question

Perimeter of rhombus is 40 one diagonal is 16 find the area of rhombus and second diagonal

Answer 1

Answer:

Perimeter = 40

Let the length of side be a:

➡ a + a + a + a = 40

➡ 4a = 40

➡ a = 40 / 4

➡ a = 10

Let the second diagonal be x.

Diagonals of rhombus bisect each other at 90 degree, using pythagoras theorem:

➡ (1st dia/2)^2 + (2nd dia/2)^2 = a^2

➡ (16/2)^2 + (x/2)^2 = 10^2

➡ 8^2 + (x/2)^2 = 100

➡ (x/2)^2 = 100-64

➡ (x/2)^2 = 36

➡ x = 12

Other diagonal is 12 and hence area is

➡ 1/2 * product of diagonals

➡ 1/2 * 12 * 16 = > 12 * 8

➡ 96

Second diagonal = 12

Area of rhombus = 96