Latest Elitmus Aptitude Question SOLUTION: If the perimeter of a rhombus is 52 cm and one of its diagonals is 24 cm, then the area of the rhombus is

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(#M40155260) ELITMUS Category question ss Keep an EYE

If the perimeter of a rhombus is 52 cm and one of its
diagonals is 24 cm, then the area of the rhombus is

Asked In Elitmus MohanRaj (8 years ago)

Unsolved Read Solution (5)

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Jyothi Prakash Thaduri  (8 years ago)

perimeter of rhombus = 4a (with side a)
4a=52 then a=13,
lets length of one diagonal p=24cm,
lenght of other diagonal is q;
area of rhombus = pq/2
using pythogorus theorem a^2= (p/2)^2 + (q/2)^2
we will get q=10.
then area=10*24/2=120 sq.cm

Is this solution Helpfull? Yes (7) | No   

JUGAL KHAJURIYA  (8 years ago)

perimeter of rhombus = 4a (with side a)
4a=52 then a=13,
lets length of one diagonal p=24cm,
lenght of other diagonal is q;
area of rhombus = pq/2
using pythogorus theorem a^2= (p/2)^2 + (q/2)^2
we will get q=10.
then area=10*24/2=120 sq.cm

Is this solution Helpfull? Yes (3) | No (1)  

Noorsaba Bano  (8 years ago)

perimeter=4a
52=4a
a=13(side)
we know that area of the rhombus is
A=1/2*d1*rootunder(4*a^2-d1^2)
= 1/2*24*rootunder(4*(13)^2-(24)^2)
= 12*10
=120cm^2

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Shubham kumar  (7 years ago)

Diagonals of a rhombus bisect each other at 90 degrees
Half of each diagonal and one side would for a right angled triangle with the side of the rhombus as the hypotenuse

One side is 52cm/4 = 13cm
Half of given diagonal is 5cm

Half of the other diagonal is √(13² - 5²) = 12cm

The other diagonal is 12cm×2 = 24cm

Area of rhombus = half product of diagonals = (1/2) × 10cm × 24cm = 120cm²

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Nikita  (6 years ago)

Perimeter =4a
4a=52
a=13
Diagonals of a rhombus bisect each other at right angles
So the triangles due to intersection of Diagonals will be right triangles
So we can get another diagonal as 13*13-12*12=5
Hence another diagonal =2*5=10
Area of rhombus =half*d1*d2=1/2*24*10=120

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