Question

12. Sum of the squares of adjacent sides of a
parallelogram is 130 sq cm and length of
one of its diagonals is 14 cm. Find the length
of the other diagonal.
Solution :​

Answer 1

Answer:

8 cm

Explanation:

Given that:

AB^2+AD^2=130°

and BD=14 cm

Diagonals of a llgm bisect each other which is the mid point of AC and BD

In a traingle ABD,point O is the mid point of side BD

BO=OD

1/2BD=7cm

AB^2+AD^2=2AO^2+2AO^2

130°=2AO^2+2(7)^2

130°=2AO^2+98

2AO^2=32

AO^2=16

AO=4 cm

Hence AC=2AO

=2×4 = 8 cm

_____________

The lenght of other diagonal is 8 cm

Answer 2

Answer :- 8 cm

Given :-

• Sum of squares of adjacent sides of a  parallelogram = 130 cm^2

• Length of 1 diagonal = 14 cm

To Find :-

Length of other diagonal

Solution :-

Let the sides of parallelogram be AB, BC, CD and DA.

Now,

(AD + DC)^2 + (AB + BC)^2 = 130 (Given)

we know that sum of squares of diagonals is equal to sum of sides of the parallelogram.

Therefore,

(AD + DC)^2 + (AB + BC)^2 = AC^2 + BD^2

130 + 130 = 14^2 + BD^2

260 = 196 + BD^2

260 - 196 = BD^2

64 = BD^2

BD = √64

BD = 8

--------------------------

Length of other diagonal is 8 cm.