Question

If the altitude of a triangle is increased by 10% while its area remains the same its corresponding base will have to be decreased by
(Α) 10%
(B) 9%
(C) $9\dfrac{1}{{11}}\% $
(D) $11\dfrac{1}{9}\% $

Answer 1

Hint:
The initial base is 100 and altitude is also 100.
Then, area$ = b \times h$. where, b is equal to base and h is equal to altitude of a triangle. Then, find the area when altitude is increased by 10% and equate both areas to find a new base.

Complete step by step solution:
Given that, base = 100
And altitude = 100
The initial base is 100 and altitude is 100.
Then,
$\text{Area}= \text{base} \times \text{Altitude}$
$⇒ Area = 100 \times 100$
$⇒ Area = 10000$.
Now,
Given, altitude is increased by 10%
 $ = 100 + \dfrac{{10}}{{100}} \times 100$
$= 110$.
Let new base be x
then,
New area = base × altitude
$= 110 \times x$
$= 110x$.
Now,
Area remain same
10000 = 110x
⇒ $x = \dfrac{{100}}{{11}}$
Altitude decrease from 100 to $\dfrac{{1000}}{{11}}$
then,
Decrease in altitude = 100 − $\dfrac{{1000}}{{11}}$
 $ = \dfrac{{1100 - 1000}}{{11}}$
= $\dfrac{{100}}{{11}} = 11\dfrac{1}{9}$
So, decrease in altitude is $11\dfrac{1}{9}\% $

Note:
In this type of question first find out, area = base × altitude and then new area = 110x and since area is same, equate them.
⇒ 10000 = 110x
⇒ $x = \dfrac{{1000}}{{11}}$
and found Decrease in altitude = 100 − $\dfrac{{1000}}{{11}}$
= $11\dfrac{1}{9}\% $