BECE Mathematics 2012 Paper

Perimeter is the sum of all the dimension of the sides of a shapePerimeter of the shape $= 25 \text{ cm} + 24 \text{ cm} +$ half the circumference of the circular portionCircumference $= 2 \pi r$Where $r =$ radius.Diameter $= 2 x$ radiusCircumference $= \pi x$ diameterLength of the circular portion $= \frac{\text{Circumference}}{2}$Length of the circular portion $= \frac{\pi x \text{ diameter}}{2}$Perimeter of the shape $= 25 \text{ cm} + 24 \text{ cm} + \frac{\pi x \text{ diameter}}{2}$ But perimeter $= 71$$71 \text{ cm} = 25 \text{ cm} + 24 \text{ cm} + \frac{\pi x \text{ diameter}}{2}$$71 = 49 + \frac{\pi x \text{ diameter}}{2}$$71 - 49 = \frac{\pi x \text{ diameter}}{2}$$22 = \frac{\pi x \text{ diameter}}{2}$Multiply both sides of the equation by 2 to get rid of the denominator 2 .$22 \times 2 = \pi \times$ diameterBut $\pi = \frac{22}{7}$$22 \times 2 = \frac{22}{7} \times$ diameter Get rid of the fraction by multiplying both sides of the equation by the denominator 7$22 \times 2 \times 7 = 22 \times$ diameterDivide both sides by 22 to make diameter the subject$\text{ Diameter } = \frac{22 \times 2 \times 7}{22} = 2 \times 7 = 14 \text{ cm}$