Test: Pythagoras Theorem - CAT MCQ

H² = P² + B²
H² = 81
P² + B² = 25 + 49 = 74
H²  ≠ P²+B².Therefore the sides cannot form a right triangle.

We have AB²=36 and BC²=144
Adding both the squares we get 
AB²+BC²=36+144=180
=AC²
So , AC is the hypotenuse according to pythagoras theorem , So the angle opposite to it which is B is 90 degrees.

Since the triangle is a right angled triangle,
Applying Pythagoras Theorem,
H²=P²+B²
15²=P²+9²
P²=225-81=144
P=12

We have a TV which is a rectangle whose adjacent sides form an angle of 90 degrees so The triangle formed by the two sides and a diagonal will be a right angle. So, Applying Pythagoras Theorem,
(Diagonal)²=80²+60²=6400+3600=10000
Diagonal=100cm

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c².

a) 43² = 1849

   36²+18² = 1620

b) 25²  = 625

    15² + 20² =625

c) 13² = 169

    3² + 12² = 153

d) 26² = 676

    24² + 25² = 1201

so option b is correct

In triangle PMQ
Angle M = 90°
Angle P = 30°
Angle QMP + Angle MPQ + Angle PQM = 180 degree ( By angle sum property )
90 + 30 + Angle PQM = 180
Angle PQM = 180 - 120
Angle PWM = 60 Degree
QM divides Angle PQR into two equal parts .
Therefore Angle MQR = 30°

In a triangle ABC in which angle B = 90 degree
So, AB is height of the given triangle = 9 cm
Base of triangle i.e, BC = 12 cm
DE is || to BC
D is the mid point of side AB and E is the mid point of side AC
By applying pythagoras
AC² = AB² + BC²
AC² = 9^2 + 12^2
AC² = 81 + 144
AC² = 225
AC = root under 225
AC = 15 cm
E is the mid point of AC
Therefore AE = AC / 2
AE = 15 / 2
AE = 7.5 cm