Question

23. Assertion In a rhombus of side 15 cm, one of the diagonals is 20 cm long. The lenght of the other diagonal 10/6 cm.
Reason The sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
PLEASE DON'T ANSWER IF YOU DONT KNOW OTHERWISE GOD WILL PUNISH YOU​

Answer 1

Answer:

A is false; R is true

Step-by-step explanation:

By using the following:

The sum of the squares of the sides of the rhombus is equal to the sum of the square of the diagonals.

So, sum of the sq of side of rhombus :-

side = 15cm

$15^{2}+15^{2} +15^{2} +15^{2}=900$

$(diagonal1)^{2} +(diagonal2)^{2}=900$  (by using formula)

$20^{2} +(diagonal2)^{2} =900\\400+(diagonal2)^{2}=900\\(diagonal2)^{2}=900-400\\(diagonal2)^{2}=500\\(diagonal2)=\sqrt{500}\\ (diagonal2)=10\sqrt{5}$

Answer 2

Given : Assertion In a rhombus of side 15 cm, one of the diagonals is 20 cm long. The length of the other diagonal 10√6 cm.

Reason The sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

To Find : Comment on Assertion and Reason

Solution:

All the sides of a rhombus are equal

and Diagonals bisect each other perpendicularly

side² = ( d₁ /2 )² +  ( d₂ /2 )²

=> 4 * side² = d₁² + d₂²

Hence Reason is TRUE

The sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

4 * side² = d₁² + d₂²

=> 4 * 15²  = 20² + d₂²

=> 900 = 400 + d₂²

=> d₂² = 500

=> d₂ = 10√5  cm

length of the other diagonal  is not 10√6 cm.

Hence Assertion is FALSE

Reason is TRUE but Assertion is FALSE

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