Question

# A rectangle has dimensions $40m×25m$. If the length and breadth are increased by $15%$ find the percentage increases in its area.

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Solution

## Step 1: Find the area of given triangleGiven, Length $=40m$ and breadth$=25m$Hence, the area of the rectangle$=$length$×$breadth $=40×25$ $=1000sq.m$Given dimensions are increased by $15%$Step 2: Find the new area of rectangleNew Length$=$$40+15%$ of $40$ and New breadth $=$ $25+15%$ of $25$Hence new length $=$ $40+\frac{15}{100}×40=46m$New breadth $=$$25+\frac{15}{100}×25=28.75$ $m$The new area of rectangle $=46m×28.75m\phantom{\rule{0ex}{0ex}}=1322.5sq.m$Step 3: Find the percentage increase in area The percentage increase in area $=\frac{\text{NewArea-Oldarea}}{\text{Oldarea}}×100\phantom{\rule{0ex}{0ex}}=\frac{1322.5-1000}{1000}×100\phantom{\rule{0ex}{0ex}}=32.25%$ Therefore, the percentage increase in area is $32.25%$

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