Question

ABCD is a parallelogram whose diagonals intersect each other at right angles. If
the length of the diagonals is 6 cm and 8 cm, find the lengths of all the sides of
the parallelogram.
IC С
D
3x
In figure 11.21, one pair of adjacent sides of
a parallelogram is in the ratio 3:4. If one of
its angles, ZA is a right angle and diagonal
BD = 10 cm, find the
B
A
4x
(i) lengths of the sides of the parallelogram.
Fig. 11.21
(ii) perimeter of the parallelogram.
0. ABCD is a quadrilateral in which AB = CD and AD=BC. Show that it is a
parallelogram. (Hint: Draw one of the diagonals.]
193​

Answer 1

Answer:

where is the pic of that

Answer 2

Step-by-step explanation:

1)In△DAB,∠A=90°

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

2

+AB

2

=BD

2

By Phythagoreantheorem

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

2

+(4x)

2

=10

2

implies 9x^{2} + 16x^{2} = 10^{2}⟹9x

2

+16x

2

=10

2

implies 25x^{2} = 10^{2}⟹25x

2

=10

2

⟹x=

5

10

=2cm

AD=BC=3x=3×2cm=6cm

iii)AB=DC=4x=4×2cm=8cm

ABCD = 2(AB + BC)Perimeter of ABCD=2(AB+BC)

=2(8cm+6cm)

=2×14cm

=28cm

Therefore.,

Lengths of the sides of ABCD

AB=DC=8cm

AD=BC=6cm

PerimeterofABCD=28cm