Question
If the height of a triangle is decreased by 40% and its base is increased by 40% , what will be he effect on its area ?
Answer: Option C
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Let initial base = b cm and initial height = h cm.
Then , initial area = `(1/2 bh) cm^2`
New base = (140% of b) cm = `((140b)/(100)) cm = ((7b)/(5))` cm
New height = (60% of h ) cm = `((60h)/(100)) cm = ((3h)/(5))`cm
New area = `(1/2 xx (7b)/(5) xx (3h)/(5)) cm^2` = `(21/50 bh) cm^2`
Area decreased = `(1/2 bh - 21/50 bh) cm^2 = (4/50 bh) cm^2`
percentage decrease = `((4bh)/(50) xx (2)/(bh) xx 100)`% = 16%
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