Question

Write the following ratios in the reduced form.

(i) Radius to the diameter of a circle.

(ii) The ratio of diagonal to the length of a rectangle, having length 4 cm and breadth 3 cm.

(iii) The ratio of perimeter to area of a square, having side 4 cm.

Answer 1

(i)
Let the radius of the circle be r units.

Diameter of the circle = 2 × Radius of the circle = 2r units

∴ Ratio of radius to diameter of a circle = Radius of the circle : Diameter of the circle = r : 2r = 1 : 2

(ii)
Length of the rectangle, l = 4 cm

Breadth of the rectangle, b = 3 cm

Now,

Diagonal of the rectangle = $\sqrt{l^2+b^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}$ = 5 cm

∴ Ratio of diagonal to the length of the rectangle = Diagonal of the rectangle : Length of the rectangle = 5 cm : 4 cm = 5 : 4

(iii)
Side of the squre = 4 cm

Perimeter of the square = 4 × Side of the squre = 4 × 4 cm = 16 cm

Area of the squre = (Side of the square)² = (4 cm)² = 16 cm²

∴ Ratio of perimeter to area of the square = Perimeter of the square : Area of the squre = 16 : 16 = 1 : 1