Rajasthan Police Constable Model Paper 8

Question : 39 of 150

Marks: +1, -0

A question is given followed by information in three statements. You have to find out the data in which statement (s) is sufficient to answer the question and mark your answer accordingly.
What is the area of the rhombus PQRS?
I) perimeter of rhombus is 60 cm.
II) One of its diagonal is 18 cm.
III) Sum of the diagonals of the rhombus is 42 cm

Only I & II or II & III is sufficient
Only II & III is sufficient
All three are sufficient
Only III is sufficient

Validate

Solution:

By statement I
Perimeter of rhombus = 4a = 60
⇒ a = 15 cm

By statement II
One diagonal = 18 cm
We know that diagonals of a rhombus cut each other at 90 degree.
So,

OP^2 = PS^2- SO^2

So,OP2=PS2−SO2
⇒

OP^2 = 15^2−9^2

⇒OP2=152-92
⇒

OP^2

= 225 - 81 = 144
⇒ OP = 12 cm
So length of other diagonal is = 2 × 12 = 24 cm
By statement III
Sum of diagonals = 42 other diagonal = 42 - 18 = 24 cm
∴ Area of Rhombus PQRS = 1/2 × d1 × d2
⇒ 1/2 × 18 × 24 = 216 cmsq
Hence only statement III is sufficient to answer or statement I & II together.

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