Question

The diagonal of a rhombus are in the ratio 3 : 4. if its perimeter is 40 cm, find the length of the sides and diagonals of the Rhombus

Answer 1

Hello...
Answer...

Now, triangle DOC is a right - angled triangle
$AB = BC = CD = AD \\ \\ Side \: of \: the \: rhombus = \frac{1}{4} \times 40 \\ \\ (40 \: \: is \: permeter) \\ \\ = 10 \: cm \\ \\ Let \: \: BD = 3x \: \: and \: AC = 4x \\ \\ OD = \frac{3}{2} x \: \: and \: \: OC = \frac{4}{2} x \\ \\ Now, triangle DOC is a right - angled triangle.$



${(OD)}^{2} + {(OC)}^{2} = {(CD)}^{2} \\ \\ = > ( \frac { {3}^{} }{2}) {}^{2} + ( \frac{4}{2} {)}^{2} = {10}^{2} \\ \\ = > \frac{ {9x}^{2} }{4} + \frac{ {16x}^{2} }{4} = 100 \\ \\ = > {25x}^{2} = 100 \times 4 \\ \\ = > {x}^{2} = \frac{400}{25} = 16 \\ \\ = > x = 4$


Hence the diagonals bd and AC of the rhombus are 12 CM and 16 CM respectively and each side is 10 CM.

Hope it helped ☺☺☺

Answer 2

The diagonals bd and AC of the rhombus are 12 CM and 16 CM respectively and each side is 10 CM.