(a) Simplify : \(\frac{x^{2} - y^{2}}{3x + 3y}\) (b) In the diagram, PQRS is a...

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 : \((216.3588 - 54.088)cm^{2}\)

\(162.2708 cm^{2}\)

\(\approxeq 162 cm^{2}\)