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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-07-PYT-01
Pythagoras Theorem & Converse — Assignment
Chapter: Triangles
Topic: Pythagoras Theorem and Its Converse
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.
(Hypotenuse)$^2=$
  • A.sum of legs
  • B.sum of squares of legs
  • C.product of legs
  • D.difference of legs
2.
$7,24,25$ form a:
  • A.right triangle
  • B.non-right triangle
  • C.straight line
  • D.obtuse triangle
3.
If $a^2+b^2=c^2$ the triangle is:
  • A.acute
  • B.right-angled
  • C.obtuse
  • D.equilateral
4.
The hypotenuse for legs $5,12$ is:
  • A.$13$
  • B.$17$
  • C.$7$
  • D.$60$
5.
The longest side of a right triangle is the:
  • A.base
  • B.hypotenuse
  • C.altitude
  • D.median
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the hypotenuse if the legs are $5$ and $12$.
7.
Is $7,24,25$ a right triangle?
8.
A ladder $13$ m long reaches $12$ m up a wall. Find the base distance.
9.
Find the missing leg: hypotenuse $10$, one leg $6$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
A $15$ m ladder leans against a wall reaching $12$ m. How far is its foot from the wall?
11.
A rectangle has diagonal $13$ cm and one side $5$ cm. Find the other side.
12.
Two poles $6$ m and $11$ m high stand $12$ m apart. Find the distance between their tops.
13.
Find the length of the diagonal of a square of side $10$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the length of the altitude of an equilateral triangle of side $2a$.
15.
A man walks $24$ m due east, then $10$ m due north. Find his distance from the start.

Answer Key

Section A — Multiple Choice Questions
  1. (B) sum of squares of legs
  2. (A) right triangle
  3. (B) right-angled
  4. (A) $13$
  5. (B) hypotenuse
Section B — Short Answer (2 marks)
  1. $13$.
  2. Yes.
  3. $5$ m.
  4. $8$.
Section C — Short Answer (3 marks)
  1. $9$ m.
  2. $12$ cm.
  3. $13$ m.
  4. $10\sqrt2$.
Section D — Long Answer (5 marks)
  1. $\sqrt3\,a$.
  2. $26$ m.
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