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24 Jul 2022, 13:15
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E
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Difficulty:
55%
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Question Stats:
44% (02:14) correct
56%
(02:15)
wrong
based on 25
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If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, what is the area of the rhombus ?
A 54 sq. cm.
B 108 sq. cm.
C 144 sq. cm.
D 200 sq. cm.
E 216 sq. cm.
A 54 sq. cm.
B 108 sq. cm.
C 144 sq. cm.
D 200 sq. cm.
E 216 sq. cm.
jatin22
Current Student
Joined: 22 Apr 2021
Last visit: 28 Mar 2023
Posts: 55
Given Kudos: 4
Location: India
Schools: INSEAD Jan'23 intake (A$) Bayes (A) IE Sep'22 Intake (A) Haas '24 (WL) Smith (A$$) UC Davis (A$$) HEC Sept'22 Intake (D) Fuqua '24 (D)
GMAT 1: 700 Q47 V39
GRE 1: Q164 V161
Products:
Schools: INSEAD Jan'23 intake (A$) Bayes (A) IE Sep'22 Intake (A) Haas '24 (WL) Smith (A$$) UC Davis (A$$) HEC Sept'22 Intake (D) Fuqua '24 (D)
GMAT 1: 700 Q47 V39
GRE 1: Q164 V161
Posts: 55
24 Jul 2022, 13:33
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Diagonals are in the ratio 3:4, meaning the length of diagonals is 3x and 4x respectively, intersecting at right angles and dividing each other into two equal halves.
This makes a right angled triangle with the side of the rhombus as the hypotenuse.
Using Pythagorean theorum, we have (3x/2)^2 + (2x)^2 = 15^2
9(x^2)/4 + 4(x^2) = 225
x^2 = 225*4/25 = 36
x = 6
So the diagonals are 3*6 = 18, and 4*6 = 24
Area of rhombus = product of diagonals/2 = 18*24/2 = 216 sq cm
This makes a right angled triangle with the side of the rhombus as the hypotenuse.
Using Pythagorean theorum, we have (3x/2)^2 + (2x)^2 = 15^2
9(x^2)/4 + 4(x^2) = 225
x^2 = 225*4/25 = 36
x = 6
So the diagonals are 3*6 = 18, and 4*6 = 24
Area of rhombus = product of diagonals/2 = 18*24/2 = 216 sq cm
24 Jul 2022, 14:10
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Bunuel
Diagonals in a ratio of 3:4 sets us up for 3:4:5 triangles. The sides of the rhombus are 15, which is 5x, so x=3. The legs of the triangles are therefore 9*12. We have four such triangles, so the total area is:
\(4*\frac{1}{2}*9*12 = 18*12 = 216\)
Answer choice E.
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