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Mathematics

Grade6

Easy

Question

A rectangular sheet of paper is $15 fraction numerator 3 over denominator 4 end fraction$ cm long having a perimeter of $56 fraction numerator 1 over denominator 2 end fraction$ cm; find its area.

$176 \frac{7}{8}$
$12 \frac{1}{2}$
$196 \frac{7}{8}$
$196 \frac{7}{15}$

hint Hint:

Area of rectangle is length $cross times$ breadth

The correct answer is: $196 fraction numerator 7 over denominator 8 end fraction$

Length of a rectangular sheet = $15 fraction numerator 3 over denominator 4 end fraction$ cm
Perimeter of the sheet = $56 fraction numerator 1 over denominator 2 end fraction$
Let the width of the sheet be x cm.
Then $2 open parentheses 15 fraction numerator 3 over denominator 4 end fraction plus x close parentheses equals 56 fraction numerator 1 over denominator 2 end fraction$
$rightwards double arrow 15 fraction numerator 3 over denominator 4 end fraction plus x equals fraction numerator 56 fraction numerator 1 over denominator 2 end fraction over denominator 2 end fraction equals fraction numerator 113 over denominator 4 end fraction$
$therefore x equals fraction numerator 113 over denominator 4 end fraction minus 15 fraction numerator 3 over denominator 4 end fraction equals fraction numerator 113 over denominator 4 end fraction minus fraction numerator 63 over denominator 4 end fraction equals fraction numerator 25 over denominator 2 end fraction equals 12 fraction numerator 1 over denominator 2 end fraction c m$
$therefore$ Width of the sheet $equals 12 fraction numerator 1 over denominator 2 end fraction c m$
Area of a rectangular sheet = $15 fraction numerator 3 over denominator 4 end fraction cross times 12 fraction numerator 1 over denominator 2 end fraction equals fraction numerator 63 over denominator 4 end fraction cross times fraction numerator 25 over denominator 2 end fraction equals fraction numerator 1575 over denominator 8 end fraction text or end text 196 fraction numerator 7 over denominator 8 end fraction$

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