Question

If the altitude of a triangle is increased by $10$% while its area remains same, its corresponding base will have to be decreased by:

• A. $10$%
• B. $9$%
• C. $9\frac{1}{11}$%
• D. $11\frac{1}{9}$%

Answer 1

The correct option is D $11\frac{1}{9}$%

Let initial base is $100$ and altitude is also $100$

Area $=100\times 100=10000$

New base increased by $10\%$ $=$$100+\frac{10}{100}\times 100=110$

Let new altitude $=x$

New area $=110x$

Area remains same ,

$10000=110x$

$x=\frac{10000}{110}$

$x=\frac{1000}{11}$

Altitude decrease from $100$ to $\frac{1000}{11}$

Decrease in altitude $=100-\frac{1000}{11}=\frac{100}{11}=11\frac{1}{9}$

So decrease in altitude is $11\frac{1}{9}\%$