Question

If each side of a triangle is halved then its perimeter will be decreased by

(A) 100% (B) 50% (C) 25% (D) none

Plz write option number. ​

Answer 1

Answer:

50%(B)

Step-by-step explanation:

o do this you can enter specific values for each sie of this triangle

for he sake of this quesion i will use even numbers

side a = 4cm

side b = 6cm

side c = 10cm

Perimeter = 4 + 6 + 10 = 20cm

half of 4 = 2

half of 6 = 3

half of 10 = 5

perimeter = 2 + 3 + 5 = 10cm

to find percentage decrease is

$\frac{decrease}{original}$×100

=$\frac{20 - 10}{20}$ ×100

=$\frac{10}{20}$×100

= 10×5

=50%(B)

this proves that if the sides are halved the perimeter is halved as well

Answer 2

Answer:

The perimeter of the triangle is reduced by 50%.

Therefore, the option (B) is correct.

Step-by-step explanation:

Consider that the sides of the triangle are a, b and c.

Perimeter of the triangle is sum all three sided of the triangle.

Perimeter of Δ $= a +b+c$

Now, if the each side will be halved then, new perimeter P':

$P'=\frac{a}{2} +\frac{b}{2} +\frac{c}{2}$

$P'=\frac{1}{2} (a+b+c)$

$P'=\frac{P}{2}$

Percentage change in perimeter $=\frac{P'-P}{P}*100$

$=(\frac{P'}{P} -1)*100$

$=(\frac{1}{2} -1)*100$

$=(\frac{-1}{2})*100$

$=-50$%

Here, the negative sign shows that the new perimeter of the triangle is reduced by 50%.