Rectangle and triangle area comparison

Rectangle and triangle area comparison

Secondary 2
6 marks
TGM Original Questions

Optional extension

A rectangle has dimensions \((3x+4)\) cm by \((x+2)\) cm. A right-angled triangle has base \((2x+3)\) cm and height \(2x\) cm. The rectangle area is \(52\text{ cm}^2\) greater.

  1. Show that \(x^2+7x-44=0\).[2]
  2. Solve for the valid \(x\).[2]
  3. Find the rectangle perimeter.[2]

Solution:

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Answer:(ii) \(x=4\) (iii) \(44\) cm. (i) \(x^2+7x-44=0\) (shown).

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