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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-07-ARE-01
Area of Similar Triangles — Assignment
Chapter: Triangles
Topic: Area of Similar Triangles
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The ratio of areas of similar triangles equals:
  • A.side ratio
  • B.(side ratio)$^2$
  • C.perimeter ratio
  • D.angle ratio
2.
Sides ratio $2:3$ gives area ratio:
  • A.$2:3$
  • B.$4:9$
  • C.$8:27$
  • D.$6:9$
3.
Area ratio $9:16$ gives side ratio:
  • A.$9:16$
  • B.$3:4$
  • C.$3:8$
  • D.$81:256$
4.
Similar triangles of equal area are:
  • A.congruent
  • B.unequal
  • C.right
  • D.larger
5.
Ratio of areas $=$ ratio of squares of corresponding:
  • A.sides
  • B.medians
  • C.altitudes
  • D.all of these
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Sides are in ratio $3:5$; find the ratio of areas.
7.
Areas are in ratio $16:25$; find the ratio of sides.
8.
Similar triangles with side ratio $1:2$ have area ratio:
9.
Areas are $36$ and $64$ cm$^2$; find the ratio of sides.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Two similar triangles have areas $81$ cm$^2$ and $144$ cm$^2$; a side of the smaller is $9$ cm. Find the corresponding side of the larger.
11.
The areas of two similar triangles are in ratio $25:36$. Find the ratio of perimeters.
12.
$\triangle ABC\sim\triangle DEF$ with areas $64$ and $121$; if $BC=8$, find $EF$.
13.
The ratio of areas of two similar triangles is $4:9$; a median of the first is $10$. Find the corresponding median.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The areas of two similar triangles are $100$ cm$^2$ and $49$ cm$^2$. If the altitude of the bigger is $5$ cm, find the corresponding altitude of the smaller.
15.
In similar triangles $ABC$ and $PQR$, $AB=2\,PQ$. If area of $PQR$ is $30$ cm$^2$, find the area of $ABC$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) (side ratio)$^2$
  2. (B) $4:9$
  3. (B) $3:4$
  4. (A) congruent
  5. (D) all of these
Section B — Short Answer (2 marks)
  1. $9:25$.
  2. $4:5$.
  3. $1:4$.
  4. $3:4$.
Section C — Short Answer (3 marks)
  1. $12$ cm.
  2. $5:6$.
  3. $11$.
  4. $15$.
Section D — Long Answer (5 marks)
  1. $3.5$ cm.
  2. $120$ cm$^2$.
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