Question

Jaffar has a square canvas with sides of 60cm length. He wants to turn it into a rectangle by reducing one pair of opposite sides, but he does not want to decrease the area by more than 10%. By how much can he reduce the length of one pair of opposite sides of the square?

• A. Reduction ≤ 6 cm
• B. Reduction < 9 cm
• C. Reduction ≤ 7 cm
• D. Reduction < 8 cm

Answer 1

The correct option is A Reduction ≤ 6 cm

Let the reduction in the length of one pair of opposite sides of the square is $x$ cm
New length of one pair of opposite sides$=(60-x)$ cm

$\mathrm{Area}\mathrm{of}\mathrm{the}\text{'}\mathrm{Square}\text{'}=60\times 60=3600{\mathrm{cm}}^2\mathrm{Area}\mathrm{of}\mathrm{the}\text{'}\mathrm{Rectangle}\text{'}\ge 90\%\mathrm{of}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\text{'}\mathrm{Square}\text{'}\Rightarrow 60(60-x)\ge \frac{90}{100}\times 3600\Rightarrow 60(60-x)\ge 3240\mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}60,\mathrm{we}\mathrm{get},\frac{60(60-x)}{60}\ge \frac{3240}{60}\Rightarrow (60-x)\ge 54cmor,x\le 60-54\mathrm{Therefore}\mathrm{reduction}\le 6\mathrm{cm}$