If such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of is 25 cm, then the perimeter of is:

If such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of is …

MCQ

If $\triangle\text{ABC}\sim\triangle\text{DEF}$ such that $\text{AB} = 9.1\ cm$ and $\text{DE} = 6.5\ cm.$ If the perimeter of $\triangle\text{DEF}$ is $25\ cm,$ then the perimeter of $\triangle\text{ABC}$ is:

A
$36\ cm.$
B
$30\ cm.$
C
$34\ cm.$
✓
$35\ cm.$

✓

Answer

Correct option: D.

$35\ cm.$

Given: $\triangle\text{ABC}$ is similar to $\triangle\text{DEF}$ such that $\text{AB}= 9.1\ cm, \text{DE} = 6.5\ cm.$ Perimeter of $\triangle\text{DEF}$ is $25\ cm.$
To find: Perimeter of $\triangle\text{ABC}.$
We know that the ratio of corresponding sides of similar triangles is equal to the ratio of their perimeters.
Hence,
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{AC}}{\text{DE}}=\frac{\text{P1}}{\text{P2}}$
$\frac{\text{AB}}{\text{DE}}=\frac{\text{P}(\triangle\text{ABC})}{\text{P}(\triangle\text{DEF})}$
$\frac{9.1}{6.5}=\frac{\text{P}(\triangle\text{ABC})}{25}$
$\text{P}(\triangle\text{ABC})=\frac{9.1\times25}{6.5}$
$\text{P}(\triangle\text{ABC})=35\text{cm}$
Hence the correct answer is $D.$