the height of a triangle is increased by 30%.what can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 90%?
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Let the height be h nd base be b
Height increases 40%, so new height = h+40% of h=7/5*h
Area of triangle= (1/2*h*b)
Area increases by 60% so , new area,
=(1/2*h*b)+60% of (1/2*h*b)
=8/5*1/2*h*b
Let new base be x, then
New area,=1/2*7/4*x
⠀⠀⠀⠀⠀⠀ =8/5*1/2*b*h
Which will result into x= 8/7*b
So, base will increase by 1/7th of b=14.2
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