Question

Shalini wants to make a toran for Diwali using some pieces of cardboard. She cut some cardboard pieces as shown below. If perimeter of ADE and BCE are in the ratio 2 : 3, then answer the following questions.
1. If the two triangles here are similar by SAS similarity rule, then their corresponding proportional
sides are
2.Length of AD =
3.Length of ED =
4.Length of AE =
step by step explanation please​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given: Shalini wants to make a toran for Diwali using some pieces of cardboard. She cut some cardboard pieces as shown below. If perimeter of ADE and BCE are in the ratio 2 : 3.

To find: Answer the following questions.

1. If the two triangles here are similar by SAS similarity rule, then their corresponding proportional sides are

2.Length of BC =

3.Length of AD =

4.Length of ED =

5.Length of AE =

Solution:

1. If the two triangles here are similar by SAS similarity rule, then their corresponding proportional sides are:

Because, it is given that $∆ADE \sim ∆BCE$Thus, corresponding sides are in proportion.

$\bf \frac{AD}{BC}=\frac{DE}{CE}=\frac{AE}{BE}$

2.Length of BC =

Ans: Length of BC can be calculated using Pythagoras theorem.

As, ∆BCE is right triangle; apply Pythagoras theorem

$BC²=CE²+BE²$

$BC²=16+9$

$BC²=25$

$\bf BC=5\:cm$

3.Length of AD =

Ans. Because sides of similar triangles are in proportion,

Therefore,

Perimeter of corresponding triangles are also in proportion.

$\frac{AD}{BC}=\frac{AD+DE+AE}{BC+CE+BE}$

$\frac{AD}{BC}=\frac{2}{3}$

$\frac{AD}{5}=\frac{2}{3}$

$\bf AD=\frac{10}{3}\:cm$

4.Length of ED =

Ans:$\frac{ED}{CE}=\frac{AD+DE+AE}{BC+CE+BE}$

$\frac{ED}{CE}=\frac{2}{3}$

$\frac{ED}{4}=\frac{2}{3}$

$\bf ED=\frac{8}{3}\:cm$

5.Length of AE =

Ans:

$\frac{AE}{BE}=\frac{AD+DE+AE}{BC+CE+BE}$

$\frac{AE}{BE}=\frac{2}{3}$

$\frac{AE}{3}=\frac{2}{3}$

$\bf AE=2\:cm$

Final answer:

1. If the two triangles here are similar by SAS similarity rule, then their corresponding proportional sides are:$\frac{AD}{BC}=\frac{DE}{CE}=\frac{AE}{BE}$

2.Length of BC = 5 cm

3.Length of AD = 10/3 cm

4.Length of ED = 8/3 cm

5.Length of AE = 2 cm

Hope it helps you.

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