Question

In figure 11.21, one pair of adjacent sides of parallelogram is in the ratio 3 : 4. If one of its angles, ZA is a right angle and diagonal a 3x BD = 10 cm, find the- lengths of the sides of the parallelogram. А B (0) 4x (ii) perimeter of the parallelogram. Fig. 11.21​

Answer 1

Answer:

Lengths of the sides of ABCD,

AB=DC=8cm

AD=BC=6cm

Perimeter of ABCD = 28cm.

Given:

ABCD is a parallelogram .

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

∠A=90°anddiagonal.

BD = 10cm.

Solution:

ABCD is a rectangle .

( One angle in a parallelogram is right angle )

i ) In angle A = 90degree In△DAB,∠A=90°

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

By Phythagorean theorem,

(3x)^{2} + (4x)^{2} = 10^{2}⟹(3x)

2 +(4x) 2=10 2

9x^{2} + 16x^{2} = 10^{2}⟹9x

2 +16x 2 = 10 2

\implies 25x^{2} = 10^{2}⟹25x

2

=10

2

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

2 = ( 5/10) 2

x = 5/10 = 2cm

ii) AD=BC=3x=3×2cm=6cm

iii) AB=DC=4x=4×2cm=8cm

= 2 (8cm+6cm)

= 2×14cm

= 28cm.

Therefore,

Lengths of the sides of ABCD,

AB=DC=8cm

AD=BC=6cm

Perimeter of ABCD = 28cm.

$thank \: you$

Answer 2

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