(a) Simplify : (frac{x^{2} – y^{2}}{3x + 3y})
(b)
In the diagram, PQRS is a rectangle. /PK/ = 15 cm, /SK/ = /KR/ and <PKS = 30°. Calculate, correct to three significant figures : (i) /PS/ ; (ii) /SK/ and (iii) the area of the shaded portion.
Explanation
(a) (frac{x^{2} – y^{2}}{3x + 3y})
(frac{(x + y)(x – y)}{3(x + y)}) (Using difference of two squares)
= (frac{x – y}{3})
(b)(i)
(sin 37 = frac{/PS/}{15})
(/PS/ = 15 times 0.6018)
= (9.03 cm)
(ii) (cos 37 = frac{/SK/}{15})
(/SK/ = 15 times 0.7986)
= (11.98 cm )
(approxeq 12.0 cm)
(iii) Area of the shaded portion = Area of rectangle PQRS – Area of triangle PSK.
/SR/ = 2(/SK/) = 2(11.98)
= 23.96 cm
Area of rectangle PQRS = (23.96 times 9.03 )
= (216.3588 cm^{2})
Area of triangle PKS = (frac{1}{2} times 11.98 times 9.03)
= (54.088 cm^{2})
Area of shaded portion : ((216.3588 – 54.088)cm^{2})
(162.2708 cm^{2})
(approxeq 162 cm^{2})