Find the diagonal of a square plot whose area is 600 m2 more than the area of a rectangular plot that has a length and breadth ratio of 5 : 2. A side of the square plot is 60% larger than the breadth of the rectangular plot.?

Question

Find the diagonal of a square plot whose area is 600 m2 more than the area of a rectangular plot that has a length and breadth ratio of 5 : 2. A side of the square plot is 60% larger than the breadth of the rectangular plot.?

√2 × 160 m
160 m
√2 × 320 m
√2 × 180 m
None of these

LohaHridoy

10 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 1 : √2 × 160 m

Given:

Square plot area is 600 m² more than the area of the rectangular plot

Rectangular plots length and breadth ratio is 5 : 2.

Each side of the square plot is 60% larger than the breadth of the rectangular plot.

Concept:

Diagonal of square = √2 × side

Area of rectangle = length × breadth

Area of square = side²

Calculation:

Let length and breadth 5x m., 2x m. respectively.

And the side of the square is 60% larger than the breadth of the rectangular plot, so

Side = 160% of (2x)

⇒ 3.2x m.

Area of rectangular plot + 600 m² = Area of square plot

⇒ (5x) × (2x) + 600 = (3.2x)²

⇒ 10x² + 600 = 10.24x²

⇒ x² = 2500

⇒ x = 50

Side of square = 3.2 × 50

⇒ 160 m

Diagonal of square = √2 × 160 m.

∴ The diagonal of the square is √2 × 160 m.