Question

in figure 11.21 one pair of adjacent sides of a parallelogram is in the ratio 3 : 4 if one of its angles angle -A is a right angle and a diagonal bd =10cm find the-
1.lengths of the sides of the parallelogram.
2.perimeter of the parallelogram.

Answer 1

Answer:

$\red { Lengths \:of \: the \:sides \:of \:ABCD }$

$\green {AB = DC = 8\:cm }$

$\green { AD = BC = 6\:cm}$

$\red { Perimeter \:of \:ABCD }\green {=28\:cm }$

Step-by-step explanation:

Given:

ABCD is a parallelogram .

One pair of adjacent sides ABCD is in the ratio 3:4.

$\angle A = 90\degree \:and \: diagonal \\BD= 10\:cm$

Solution:

ABCD is a rectangle .

( One angle in a parallelogram is right angle )

$i ) In \: \triangle DAB , \:\angle A = 90\degree$

$AD^{2} + AB^{2} = BD^{2}$

$\pink { By \: Phythagorean \:theorem)}$

$\implies (3x)^{2} + (4x)^{2} = 10^{2}$

$\implies 9x^{2} + 16x^{2} = 10^{2}$

$\implies 25x^{2} = 10^{2}$

$\implies x^{2} = \left(\frac{10}{5}\right)^{2}$

$\implies x = \frac{10}{5} = 2\:cm$

$ii) AD = BC = 3x = 3\times 2\:cm = 6\:cm$

$iii) AB = DC = 4x = 4\times 2\:cm = 8\:cm$

$Perimeter\: of \: ABCD = 2(AB + BC)$

$= 2( 8\: cm + 6\:cm )\\= 2 \times 14\:cm \\= 28\:cm$

Therefore.,

$\red { Lengths \:of \: the \:sides \:of \:ABCD }$

$\green {AB = DC = 8\:cm }$

$\green { AD = BC = 6\:cm}$

$\red { Perimeter \:of \:ABCD }\green {=28\:cm }$

•••♪

Answer 2

Step-by-step explanation:

hope it will help

ans -6,8