CUET UG 2025 — General Test Geometry

2025mcqeasy

The sides of a triangle are in the ratio of $\frac{1}{4}:\frac{1}{5}:\frac{1}{6}$ . If the perimeter of the triangle is 37 cm, then find the length of the greatest side of the triangle?

Official previous-year question

Held on 28 May 2025 · Verified 13 Jul 2026.

Options

A
10 cm
B
15 cm
C
12 cm
D
17 cm

Did you get this right?

Solution

The triangle has sides in the ratio $\dfrac{1}{4}:\dfrac{1}{5}:\dfrac{1}{6}$ .

To simplify, find the LCM of the denominators 4, 5, and 6.

$4 = 2^2$ , $5 = 5$ , $6 = 2 \times 3$

$\text{LCM} = 2^2 \times 3 \times 5 = 60$

Multiply each fraction by 60:

$\dfrac{1}{4} \times 60 = 15$

$\dfrac{1}{5} \times 60 = 12$

$\dfrac{1}{6} \times 60 = 10$

The simplified ratio of the sides is $15:12:10$ .

Let the common multiplier be $x$ .

First side $= 15x$

Second side $= 12x$

Third side $= 10x$

The perimeter is $37$ cm.

$15x + 12x + 10x = 37$

$37x = 37$

$x = 1$

The greatest side corresponds to the largest ratio value, which is $15x$ .

Greatest side $= 15 \times 1 = 15$ cm

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Solution

The triangle has sides in the ratio $\dfrac{1}{4}:\dfrac{1}{5}:\dfrac{1}{6}$ .

To simplify, find the LCM of the denominators 4, 5, and 6.

$4 = 2^2$ , $5 = 5$ , $6 = 2 \times 3$

$\text{LCM} = 2^2 \times 3 \times 5 = 60$

Multiply each fraction by 60:

$\dfrac{1}{4} \times 60 = 15$

$\dfrac{1}{5} \times 60 = 12$

$\dfrac{1}{6} \times 60 = 10$

The simplified ratio of the sides is $15:12:10$ .

Let the common multiplier be $x$ .

First side $= 15x$

Second side $= 12x$

Third side $= 10x$

The perimeter is $37$ cm.

$15x + 12x + 10x = 37$

$37x = 37$

$x = 1$

The greatest side corresponds to the largest ratio value, which is $15x$ .

Greatest side $= 15 \times 1 = 15$ cm

CUET UG 2025 — General Test Geometry

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Did you get this right?

Solution

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CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

More CUET UG Geometry questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

Quantitative Reasoning

Current Affairs

Keep practicing Geometry