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Which of the following cannot be the sides a right triangle?
H^{2 }= P^{2 }+ B^{2}
H^{2} = 81
P^{2 }+ B^{2 }= 25 + 49 = 74
H^{2 } ≠ P^{2}+B^{2}.Therefore the sides cannot form a right triangle.
In a triangle ABC, AC= √180, AB = 6, BC = 12. What is ∠B = ?
We have AB^{2}=36 and BC^{2}=144
Adding both the squares we get
AB^{2}+BC^{2}=36+144=180
=AC^{2}
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,
H^{2}=P^{2}+B^{2}
15^{2}=P^{2}+9^{2}
P^{2}=22581=144
P=12
Three squares are based on the sides of a right angled triangle. The area of the two smaller ones are 144 sq. cm and 256 sq. cm. What is the area of the third one?
What is the diagonal length of a TV screen whose dimensions are 80 x 60 cm?
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}=80^{2}+60^{2}=6400+3600=10000
Diagonal=100cm
A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c².
a) 43^{2} = 1849
36^{2}+18^{2} = 1620
b) 25^{2 }= 625
15^{2 }+ 20^{2} =625
c) 13^{2} = 169
3^{2} + 12^{2} = 153
d) 26^{2} = 676
24^{2} + 25^{2} = 1201
so option b is correct
QM ⊥ RP and PR^{2} – PQ^{2} = OR^{2}. If∠QPM = 30°, Then ∠MQR is
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 the above figure, AB = c, BC = a, AC = b, AD = y, DB = p. Check which of the following options is correct ?
In right triangled ABC right angled at B, a line DE is drawn through the mid point D of AB and parallel to BC. If AB = 9 cm, BC = 12 cm. AE = ?
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
AC^{2} = AB^{2} + BC^{2}
AC^{2} = 9^2 + 12^2
AC^{2} = 81 + 144
AC^{2} = 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
A boy is trying to catch fish sitting at a height of 12 m from the surface of the water. A big fish is at a horizontal distance of 5 m from him. What should be the length of his string to get the fish?
Three numbers form a Pythagorean triplet. Two of them are 15 and 17 where 17 is the largest of them. The third number is
Triangle PQR is an isosceles right triangle right angled at Q. If PR = √50. What is the value of each of the equal sides?
The length of an altitude of an equilateral triangle of side a is:
Two friends A and B start from the same point in the Eastern and Northern directions at the same time. How far are they from each other when A has travelled 5 km and B has travelled 12 km. distance?
Two similar right triangles ABC and PQR are as shown in the figure.If AB = √3 , PQ = √3/2,BC = 1. Find PR = ?
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