Theory question 110
Algebraic Expressions(a) Simplify (x2 − y2)/(3x + 3y)
(b) In the diagram, PQRS is a rectangle. |PK| = 15 cm, |SK| = |KR| and PK̂S = 37°. Calculate, correct to three significant figures: (i) |PS|; (ii) |SK|; (iii) the area of the shaded portion.
Show the model answer
Model answer
(a) (x − y)(x + y)/3(x + y) = (x − y)/3.
(b)(i) |PS| = 15 sin 37° ≈ 9.03 cm.
(ii) |SK| = 15 cos 37° ≈ 12.0 cm (11.98 cm).
(iii) |SR| = 2 × 11.98 = 23.96 cm. Rectangle = 23.96 × 9.027 ≈ 216.3 cm2; ΔPSK = ½ × 11.98 × 9.027 ≈ 54.1 cm2.
Shaded area ≈ 216.3 − 54.1 ≈ 162 cm2.
Explanation
The shaded part is the rectangle minus the right triangle PSK.