All the lengths in this question are in centimetres. The diagram shows a shape $$\(A B C D E F\)$$ made from two rectangles. The total area of the shape is $$\(342 \mathrm{~cm}^{2}\)$$. Show that $$\(x^{2}+x-72=0\)$$.
Exam No：0580_s20_qp_43 Year：2020 Question No：5(a)
Answer:
\((4 x-5)(x+3)+(x+1)(x-3)=342\)
or
\(2 x(4 x-5)-(3 x-6)(x-3)=342\)
\(4 x^{2}+12 x-5 x-15\) oe and
\(x^{2}+x-3 x-3\) oe seen
\(\mathrm{OR}\)
\(8 x^{2}-10 x\) and \(3 x^{2}-15 x+18\) seen
\(5 x^{2}+5 x-18=342\) leading to
\(x^{2}+x-72=0\)
or
\(2 x(4 x-5)-(3 x-6)(x-3)=342\)
\(4 x^{2}+12 x-5 x-15\) oe and
\(x^{2}+x-3 x-3\) oe seen
\(\mathrm{OR}\)
\(8 x^{2}-10 x\) and \(3 x^{2}-15 x+18\) seen
\(5 x^{2}+5 x-18=342\) leading to
\(x^{2}+x-72=0\)
Knowledge points:
E2.2.3 Expand products of algebraic expressions. (e.g. expand (x + 4)(x – 7)) (Includes products of more than two brackets, e.g. (x + 4)(x – 7)(2x + 1))
E5.2 Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these.
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download