Question

If the area covered by the semi-circle in the given rectangle is 77cm sq, then the ratio of the green region to the purple region is:​

Answer 1

The green is lower then the purple

Answer 2

• The ratio of the green region to the purple region is equal to 3 : 11 .

Given :- The area covered by the semi-circle in the given rectangle is 77cm² .

To Find :-

• The ratio of the green region to the purple region ?

Formula used :-

• Area of semi-circle = (1/2)•π•r² { r = radius }
• Area of rectangle = Length × Breadth .

Solution :-

Let us assume that, radius of semi-circle is equal to r cm .

So,

→ Area of purple region = 77 cm² ---- Equation (1)

→ Area of semi-circle = 77 cm²

→ (1/2)•π•r² = 77

→ (1/2) × (22/7) × r² = 77

→ (11/7) × r² = 77

→ r² = (77 × 7)/11

→ r² = 7 × 7

→ r² = 7²

square root both sides,

→ r = 7 cm

Now,

→ Length of rectangle = Diameter of semi-circle = 2•r = 2 × 7 = 14 cm

→ Breadth of rectangle = Radius of semi-circle = r = 7 cm

So,

→ Area of rectangle = Length × Breadth

→ Area of rectangle = 14 × 7

→ Area of rectangle = 98 cm² ---- Equation (2)

therefore, subtracting Equation (1) from Equation (2) we get,

→ Area of green region = Area of rectangle - Area of purple region

→ Area of green region = 98 - 77

→ Area of green region = 21 cm²

hence,

→ Area of green region : Area of purple region = 21 : 77

→ Area of green region : Area of purple region = 3×7 : 11×7

→ Area of green region : Area of purple region = 3 : 11 (Ans.)

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