Target Mathematics

1.3: Rectangle inequalities for perimeter and area

4PM1/1R/June/2025 — Question 5 · 7 marks

1.3 diagram 1
(2x+3)cm(2x + 3) \mathrm{cm}
Figure 1 shows a rectangle with width xx cm and length (2x+3)(2x + 3) cm.
The perimeter of the rectangle is PP cm and the area of the rectangle is AAcm2\mathrm{cm}^2
P>10andA<35P > 10 \quad \mathrm{and} \quad A < 35
Find the set of possible values for xx
Give your answer in the form a<x<ba < x < b where aa and bb are rational numbers.
Show clear algebraic working.
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