If the height of a triangle is decreased by 4 | vedclass

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Question

(A) The area of a triangle is given by $A = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Let the original base be $b$ and the original height

Vedclass · Accepted Answer

Decrease by $22 \%$

Vedclass · Answer

(A) The area of a triangle is given by $A = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Let the original base be $b$ and the original height be $h$. The original area is $A_1 = \frac{1}{2}bh$.After the changes,the new base $b' = b + 0.30b = 1.3b$ and the new height $h' = h - 0.40h = 0.6h$.The new area is $A_2 = \frac{1}{2} 	imes (1.3b) 	imes (0.6h) = 0.78 	imes (\frac{1}{2}bh) = 0.78A_1$.The percentage change in area is $\frac{A_2 - A_1}{A_1} 	imes 100 = (0.78 - 1) 	imes 100 = -22 \%$.Alternatively,using the net percentage change formula: $	ext{Net effect} = (x + y + \frac{xy}{100}) \% = (-40 + 30 + \frac{-40 	imes 30}{100}) \% = (-10 - 12) \% = -22 \%$.Thus,the area decreases by $22 \%$.

If the height of a triangle is decreased by $40 \%$ and its base is increased by $30 \%$,what will be the effect on the area?

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