Given △ A B C ~ △ P Q R . If A B P Q = 1 3 , then find a r △ A B C a r △ P Q R .

Given, △ A B C ~ △ P Q R and A B P Q = 1 3 We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. ∴ a r △ A B C a r △ P Q R = A B P Q 2 = 1 3 2 = 1 9 Therefore, the required answer is 1 9 .

If △ A B C ~ △ Q R P , a r △ A B C a r △ Q R P = 9 4 and B C = 15 cm , then find P R .

Given, △ A B C ~ △ Q R P , a r △ A B C a r △ Q R P = 9 4 and B C = 15 cm . We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. ∴ a r △ A B C a r △ Q R P = B C R P 2 ⇒ 15 P R 2 = 9 4 ⇒ 15 P R = 9 4 ⇒ 15 P R = 3 2 ⇒ P R = 15 × 2 3 ⇒ P R = 10 Therefore, the required answer is 10 cm .

E M B I B E

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Execise 7.3>Q 23

HARD

10th CBSE

IMPORTANT

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A street light bulb is fixed on a pole $6 m$ above the level of street. If a woman of height $1.5 m$ casts a shadow of $3 m$ , and she is $x m$ away from the base of the pole, find $x$ .

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Important Questions on Triangles

EASY

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Execise 7.4>Q 1

Given

△ A B C ~ △ P Q R

. If

\frac{A B}{P Q} = \frac{1}{3}

, then find

\frac{a r (△ A B C)}{a r (△ P Q R)}

.

EASY

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Execise 7.4>Q 2

If

△ A B C ~ △ Q R P

,

\frac{a r (△ A B C)}{a r (△ Q R P)} = \frac{9}{4}

and

B C = 15 cm

, then find

P R

.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Execise 7.4>Q 3

Question Image

In the adjoining figure, $D E ∥ B C, A D = 1 cm$ and $B D = 2 cm$ . What is the ratio of $a r (△ A B C)$ and $a r (△ A D E)$ ?

EASY

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Execise 7.4>Q 4

Areas of two similar triangles are

36 {cm}^{2}

and

100 {cm}^{2}

. If the length of a side of the larger triangle is

20 cm

, find the length of the corresponding side of the smaller triangle.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Execise 7.4>Q 5

Question Image

In the adjoining figure, $D E ∥ B C$ . If $D E = 4 cm, B C = 6 cm$ and area of $△ A D E$ is $16 {cm}^{2}$ , find the area of $△ A B C$ .

EASY

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Execise 7.4>Q 6

Question Image

In the adjoining figure, $A B ∥ D C, A O = 10 cm, O C = 5 cm, A B = 6.5 cm$ and $O D = 2.8 cm$ . Prove that $△ O A B ~ △ O C D$ .

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Execise 7.4>Q 6

Question Image

In the adjoining figure, $A B ∥ D C, A O = 10 cm, O C = 5 cm, A B = 6.5 cm$ and $O D = 2.8 cm$ . Find $C D$ and $O B$ .

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Execise 7.4>Q 6

Question Image

In the adjoining figure, $A B ∥ D C, A O = 10 cm, O C = 5 cm, A B = 6.5 cm$ and $O D = 2.8 cm$ . Find the ratios of areas of $△ O A B$ and $△ O C D$ .