CUET UG 2025 — General Test Geometry

Let width $= w$=w

The length is 5 more than twice the width, so:

Length $= 2w + 5$=2w+5

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The area of the rectangle is 75 square units.

Area $=$= Length $\times$× Width

$$75 = (2w + 5) \times w$$75=(2w+5)×w

$$75 = 2w^2 + 5w$$75=2w2+5w

$$2w^2 + 5w - 75 = 0$$2w2+5w−75=0

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Factoring the quadratic equation:

Looking for two numbers that multiply to $(2 \times -75) = -150$(2×−75)=−150 and add to $5$5.

These numbers are $15$15 and $-10$−10.

$$2w^2 + 15w - 10w - 75 = 0$$2w2+15w−10w−75=0

$$w(2w + 15) - 5(2w + 15) = 0$$w(2w+15)−5(2w+15)=0

$$(2w + 15)(w - 5) = 0$$(2w+15)(w−5)=0

$w = -7.5$w=−7.5 or $w = 5$w=5

Since width cannot be negative, $w = 5$w=5 units.

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Length $= 2w + 5$=2w+5

Length $= 2(5) + 5$=2(5)+5

Length $= 15$=15 units

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Perimeter of rectangle $= 2(\text{Length} + \text{Width})$=2(Length+Width)

Perimeter $= 2(15 + 5)$=2(15+5)

Perimeter $= 2(20)$=2(20)

Perimeter $= 40$=40 units

Therefore, the perimeter of the rectangle is 40 units.