The length of a rectangle is three-fifths of the radius of a circle. The…
2025
The length of a rectangle is three-fifths of the radius of a circle. The radius of the circle is equal to the side of the square; the area of square is 2025 m2. What is the area (in m2) of the rectangle if the breadth is 10 m?
Answer: D. 270 — ConceptArea of a square with side s is s2. Area of a rectangle is length × breadth. When a radius is stated to equal a given side length, that side length is…
- A.
200
- B.
300
- C.
135
- D.
270
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Correct answer: D
Concept
Area of a square with side s is s2. Area of a rectangle is length × breadth. When a radius is stated to equal a given side length, that side length is substituted directly as the radius.
Application
Area of the square = (side)2 = 2025 m2, so side = √2025 = 45 m.
The radius of the circle equals the side of the square, so radius = 45 m.
Length of the rectangle = three-fifths of the radius = (3/5) × 45 = 27 m.
Breadth of the rectangle is given as 10 m.
Area of the rectangle = length × breadth = 27 × 10 = 270 m2.
Cross-check
452 = 2025 confirms the side/radius value; (3/5) × 45 = 135/5 = 27 confirms the length; 27 × 10 = 270 confirms the final area. So the area of the rectangle is 270 m2.