BPSC CCE Prelims
Mensuration Previous Year Questions (PYQs)

Detailed Explanation:

Let length = l cm and breadth = b cm.

Area equation: l × b = 30
Perimeter equation: 2(l + b) = 26 ⇒ l + b = 13

From l + b = 13, we get b = 13 - l. Substituting in l × b = 30:
l(13 - l) = 30 ⇒ 13l - l² = 30 ⇒ l² - 13l + 30 = 0

Factoring: (l - 10)(l - 3) = 0 ⇒ l = 10 or l = 3

If l = 10, then b = 3; if l = 3, then b = 10.
The sides are 10 cm and 3 cm.

Detailed Explanation:

Diagonals of a rhombus bisect each other at right angles. Half-diagonals: 5 cm and 12 cm.

Using Pythagoras theorem: Side = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Perimeter = 4 × 13 = 52 cm.

Therefore, Option 1 is the correct answer.

Detailed Explanation:

A rhombus has all sides equal. With perimeter 52 m, each side = 52 ÷ 4 = 13 m. Diagonals of a rhombus bisect each other at right angles, forming four right triangles.

Taking half of the shorter diagonal = 10 ÷ 2 = 5 m and side = 13 m, applying Pythagoras theorem: half of longer diagonal = √(13² − 5²) = √(169 − 25) = √144 = 12 m. Full longer diagonal = 12 × 2 = 24 m.

Therefore, the longer diagonal is 24 m, making Option 4 the correct answer.