The area of a rectangle is 300 cm² and the length of its diagonal is 25 cm. The perimeter of the rectangle (in cm) is:

Question

Question

This question was previously asked in

NTPC CBT-I (Held On: 29 Dec 2020 Shift 2)

Answer 1

Given:

Area of rectangle = 300 cm²

Diagonal = 25 cm

FORMULA USED:

Area of a rectangle = length × breadth

Perimeter of a rectangle = 2 (length + breadth)

Diagonal = √(length2 + breadth2)

Calculation:

According to question,

⇒ length × breadth = 300

Again,

Diagonal = √(length2 + breadth2)

⇒ √(length2 + breadth2) = 25

⇒ (length2 + breadth2) = 625

Let the length be a and breadth be b

Then,

⇒ (a + b)² = a² + b² + 2ab

⇒ (a + b)² = 625 + 2 × 300

⇒ (a + b)² = 1225

⇒ a + b = 35

Perimeter of rectangle = 2(a + b)

⇒ 2 × 35

⇒ 70

∴ Perimeter of rectangle is 70.

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