Question

The height of a triangle is increased by 40%. What can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60%?

Answer 1

Answer:

The maximum %age increase must be 14.28%

New base= change in area =1.6 =1.1428

change in height 1.4

so, maximum % age increase in base is 14.28%

Answer 2

Base will increase by 1/7th of b=14.28%.

Step-by-step explanation:

Consider the provided information.

Let the height of the triangle is h and base is b.

It is given that height increased by 40%

New height = h + 40% of h

New height = $h+\frac{2}{5}h=\frac{7}{5}h$

The area of triangle is: $A=\frac{1}{2}(b\times h)$

Let new base be x, then

Thus, $A=\frac{1}{2}(x\times \frac{7}{5}h)$

The Area increases by 60%. so, new area,

$A=\frac{1}{2}(b\times h)+\frac{60}{100}\times\frac{1}{2}(b\times \frac{7}{5}h)$

$A=\frac{8}{5}\times\frac{1}{2}(b\times h)$

Substitute the value of A from above.

$\frac{8}{5}\times\frac{1}{2}(b\times h)=\frac{1}{2}(x\times \frac{7}{5}h)$

$\frac{8}{5}\times b=\frac{7}{5}x\\\\x=\frac{8}{7}b$

So, base will increase by 1/7th of b=14.28%.

#Learn more

Weight of A and B are in the ratio of 3:5. If the weight of A is increased by 20 percent and then the total weight becomes 132 kg with an increase of 10 percent. B weight is increased by what percent.

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