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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-23-APP-01
Applications of Pythagoras - Assignment
Chapter: Pythagoras Theorem
Topic: Application in Calculating Sides and Diagonals
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 diagonal of a rectangle $l\times b$ is:
  • A.$l+b$
  • B.$\sqrt{l^2+b^2}$
  • C.$lb$
  • D.$2(l+b)$
2.
The diagonal of a square of side $a$ is:
  • A.$a$
  • B.$2a$
  • C.$a\sqrt2$
  • D.$a\sqrt3$
3.
The diagonal of a $3\times4$ rectangle is:
  • A.$5$
  • B.$7$
  • C.$12$
  • D.$6$
4.
A ladder against a wall forms a right triangle with the wall and the:
  • A.roof
  • B.ground
  • C.window
  • D.sky
5.
A cuboid's space diagonal uses Pythagoras applied:
  • A.once
  • B.twice
  • C.thrice
  • D.never
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the diagonal of a rectangle $6$ by $8$.
7.
Find the diagonal of a square of side $5$.
8.
Find the diagonal of a $9$ by $12$ rectangle.
9.
A $13$ m ladder reaches $12$ m up a wall. Find the foot's distance from the wall.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the diagonal of a rectangle $12$ cm by $16$ cm.
11.
The diagonal of a square is $10\sqrt2$; find its side.
12.
A $17$ m ladder reaches a window $15$ m high. Find the foot's distance from the wall.
13.
Find the diagonal of a square of side $7$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A $10$ m ladder leans against a wall with its foot $6$ m from the wall. How high does it reach?
15.
A rectangular field is $24$ m by $32$ m. Find its diagonal and the distance saved by walking the diagonal instead of two sides.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\sqrt{l^2+b^2}$
  2. (C) $a\sqrt2$
  3. (A) $5$
  4. (B) ground
  5. (B) twice
Section B — Short Answer (2 marks)
  1. $10$.
  2. $5\sqrt2$.
  3. $15$.
  4. $5$ m.
Section C — Short Answer (3 marks)
  1. $20$ cm.
  2. $10$.
  3. $8$ m.
  4. $7\sqrt2$.
Section D — Long Answer (5 marks)
  1. $8$ m.
  2. Diagonal $40$ m; saves $16$ m.
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