2.2.4 Factorisation and Algebraic Fractions, PT3 Practice - Mathematics

Question 12:

Diagram shows a square ABCD and a right-angled triangle PQR with equal area. Based on the information, find the value of x.

Hence, find the perimeter, in cm, of the square ABCD. [4 marks]

Solution:

\begin{matrix} {(3 x + 2)}^{2} = \frac{1}{2} (4 x + 8) 4 x 9 x^{2} + 12 x + 4 = 8 x^{2} + 16 x x^{2} - 4 x + 4 = 0 (x - 2) (x - 2) = 0 x = 2 \end{matrix}

$\begin{array}{l} {(3 x + 2)}^{2} = \frac{1}{2} (4 x + 8) 4 x \\ 9 x^{2} + 12 x + 4 = 8 x^{2} + 16 x \\ x^{2} - 4 x + 4 = 0 \\ (x - 2) (x - 2) = 0 \\ x = 2 \end{array}$

Perimeter of the square ABCD

= (3x + 2) × 4

= [3 (2) + 2] × 4

= 32 cm

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