Maths-
General
Easy
Question
In a rhombus of side of 10 cm, one of the diagonals is 12 cm long. Find the length of the second diagonal.
Hint:
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2
The correct answer is: Hence, the length of the other diagonal is 16 cm.
Let ABCD be the rhombus with diagonals AC and BD intersecting each other at O.
We know that the diagonals of a rhombus bisect each other at right angles.
So, AC = 12 cm, AO = 6 cm
Applying Pythagoras theorem in right-angled triangle AOB.
AB2 = OA2 + OB2
OB2 = AB2 - OA2
OB2 = 102 - 62
OB2 = 100 − 36 = 64
OB = 
Length of other diagonal = BD = 2 OB = 16 cm
Final Answer:
Hence, the length of the other diagonal is 16 cm.
We know that the diagonals of a rhombus bisect each other at right angles.
So, AC = 12 cm, AO = 6 cm
Applying Pythagoras theorem in right-angled triangle AOB.
AB2 = OA2 + OB2
OB2 = AB2 - OA2
OB2 = 102 - 62
OB2 = 100 − 36 = 64
OB =
Length of other diagonal = BD = 2 OB = 16 cm
Final Answer:
Hence, the length of the other diagonal is 16 cm.Related Questions to study
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