Question

If $\triangle ABC \sim \triangle DEF$ such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of $\triangle DEF$ is 25 cm, then the perimeter of $\triangle ABC$ is
(a) 36 cm
(b) 30 cm
(c) 34 cm
(d) 35 cm

Answer 1

Answer:

The Perimeter of ΔABC is 35 cm.

Among the given options option (d) is 35 cm is the correct answer.

Step-by-step explanation:

Given:

ΔABC and  ΔDEF are similar  

ΔABC ~ ΔDEF  

AB = 9.1 cm

DE = 6.5 cm

Perimeter of ΔDEF ,P2= 25 cm

Let the Perimeter of ΔABC be P1  

 

AB/DE = BC/EF = CA/FD = P1/P2

[Ratio of corresponding sides of two similar triangles is equal to the ratio of the Perimeters]  

AB/DE = P1/P2

9.1 / 6.5 = P1/25

6.5 P1= 25 × 9.1

P1 = (25 × 9.1)/6.5

P1 = (5 × 91)/13

P1 = 5 × 7

P1 = 35 cm  

Hence, the Perimeter of ΔABC is 35 cm.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

$\huge\mathcal{ANSWER}$

The correct answer is option (d) .

Hence , the perimeter of triangle ABC is 35 cm .

$\huge\mathcal{SOLUTION}$

GIVEN :

☆ $\triangle ABC$ $\sim$ triangle DEF

☆ AB = 1.9 cm

☆ DE = 6.5 cm

☆ Perimeter of (P) Triangle DEF = 25 cm .

☆ Perimeter ( P ) of $\triangle ABC$ = ??

SOLVE :

AB / DE = BC / EF = AC / FD = P ($\triangle ABC$)/ P of triangle DEF

[ Ratio of the sides of two similar triangles is equal to the ratio of its perimeters ]

=> AB / DE = P ($\triangle ABC$)/ P of triangle DEF

=>1.9/6.5= P of triangle ABC / P of triangle DEF

=> P ($\triangle ABC$)= $\frac{1.9 \times 25}{6.5}$

=> P ($\triangle ABC$)= 35 cm .

Hence , the perimeter of triangle ABC is 35 cm .