Online Test — Pythagoras Theorem
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
In a right-angled triangle ABC with the right angle at corner B, side AB = 6 cm and BC = 8 cm. Find the length of AC.
14 cm
10 cm
12 cm
9 cm
Explanation: AC² = 6² + 8² = 36 + 64 = 100 -> AC = √100 = 10 cm.
Question 2 of 10
medium
Which of the following sets of side lengths forms a perfect right-angled triangle?
3, 5, 7
5, 10, 12
5, 12, 13
4, 6, 8
Explanation: 5² + 12² = 25 + 144 = 169 = 13². This satisfies the converse rule.
Question 3 of 10
medium
A rectangle has a length of 24 cm and a diagonal measuring 26 cm. Calculate the width of this rectangle.
10 cm
12 cm
8 cm
14 cm
Explanation: Width² = 26² - 24² = 676 - 576 = 100 -> Width = √100 = 10 cm.
Question 4 of 10
medium
What is the mathematical name for the longest side of a right-angled triangle?
Perpendicular
Base
Median
Hypotenuse
Explanation: The hypotenuse is defined as the longest side, sitting opposite the right angle.
Question 5 of 10
medium
Find the length of the diagonal of a square whose side length is exactly 5 cm.
10 cm
5√2 cm
25 cm
5√3 cm
Explanation: The diagonal of a square is always equal to side × √2, which gives 5√2 cm.
Question 6 of 10
medium
If a triangle has side measurements of 8 cm, 15 cm, and 17 cm, where is the 90-degree right angle located?
Opposite the 8 cm side
Opposite the 15 cm side
Opposite the 17 cm side
It has no right angle
Explanation: By the Converse Theorem, the right angle sits opposite the longest side.
Question 7 of 10
medium
An isosceles triangle has equal sides of 10 cm each and a base of 12 cm. Find its perpendicular altitude height.
8 cm
6 cm
4 cm
5 cm
Explanation: The altitude splits the base in half (6 cm). Height² = 10² - 6² = 100 - 36 = 64 -> Height = 8 cm.
Question 8 of 10
medium
A guy-wire is attached to the top of a 15-meter vertical antenna tower. The wire is anchored to the ground 8 meters from the base of the tower. How long is the wire?
23 m
17 m
20 m
16 m
Explanation: Wire² = 15² + 8² = 225 + 64 = 289 -> Wire = √289 = 17 meters.
Question 9 of 10
medium
If the hypotenuse of a right triangle is 25 cm and the perpendicular is 20 cm, find its base.
15 cm
12 cm
10 cm
18 cm
Explanation: Base² = 25² - 20² = 625 - 400 = 225 -> Base = √225 = 15 cm.
Question 10 of 10
medium
If a triangle has sides such that a² + b² > c², what type of triangle is it?
Right-angled
Obtuse-angled
Acute-angled
Equilateral
Explanation: When the sum of the squares of the shorter sides exceeds c², the triangle is acute.