# 2.2.4 Factorisation and Algebraic Fractions, PT3 Practice

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:

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

Perimeter of the square ABCD
= (3x + 2) × 4
= [3 (2) + 2] × 4
= 32 cm