Question

The perimeter of a rhombus is 52 cm and one of its diagonal is 10 cm. Find the length of a other diagonal and the area of a rhombus

Answer 1

P = 4*s

=) s = 52/4
= 13cm.

Since s^2 = (d1/2)^2 + (d2/2)^2

=) 13^2 = 5^2 + (d2/2)^2

=) 169-25=144 = (d2/2)^2

=) 12cm = d2/2

=) 24cm = d2

Since A = 1/2 * d1*d2

=) 1/2 * 10 * 24

= 120cm^2.

Hope it's helpful to u.

Answer 2

Perimeter of rhombus =4a
52=4.a
a=52/4
a=13
Half of diagonal =5cm
${h}^{2} = {b}^{2} + {p}^{2} \\ {b}^{2} = {h}^{2} - {p}^{2} \\ = {13}^{2} - {5}^{2} \\ = \sqrt{169 - 25} \\ \sqrt{144} = 12cm$
Full diagonal=24cm
Area of rhombus =1/2*D*d
=1/2*24*10
=120cm^2
Hope this will be helpful for you.