Question

the sides of a scalene triangle is halved its perimeter decreases by what percent? Plzzzzzzzzz answer this ​

Answer 1

Answer:

Explanation:

Given:

A scalene triangle whose sides are halved. What is the percentage change in its perimeter??

Let the original sides of the scalene triangle be x , y and z.

Original Perimeter = x+y+z

$Let \: the \: new \: sides \: of \: the \: scalene$

$triangle \: be \: \frac{x}{2}\:,\frac{y}{2}\:and\:\frac{z}{2}.$

$\Longrightarrow\:\:\:New \: Perimeter \: = \: \frac{x}{2} + \frac{y}{2} + \frac{z}{2}$

Taking LCM, we get:

$\Longrightarrow\:\:\:New \: Perimeter= \frac{x + y + z}{2}$

$\Longrightarrow\:\:\:\% \: change \: in \: perimeter=100\% - ( \frac{new \: perimeter}{original \: perimeter} \times 100)\%$

$\% \: change \: in \: perimeter=100\% - ( \frac{11}{20} \times 100)\%$

$\Longrightarrow\:\:\:\% \: change \: in \: perimeter=100\% - ( \frac{100}{2} )\%$

$\Longrightarrow\:\:\:\% \: change \: in \: perimeter=100\% - 50\%$

$\Longrightarrow\:\:\:\% \: change \: in \: perimeter=50\%$

Therefore, the answer is 50% decrease.