Advertisements
Advertisements
Question
Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.
Advertisements
Solution
Let ∆PQR be the given right-angled triangle.
In ∆PQR, ∠Q = 90°
∴ PR2 = PQ2 + QR2 .......[Pythagoras theorem]
∴ PR2 = 92 + 122
∴ PR2 = 81 + 144
∴ PR2 = 225
∴ PR = `sqrt(225)` .....[Taking the square root of both sides]
∴ PR = 15 cm
∴ The length of the hypotenuse of the right-angled triangle is 15 cm.
RELATED QUESTIONS
ABC is a right-angled triangle, right-angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 5 cm and 12 cm. Find the radius of the circle
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AD2 = BD × CD
ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2
ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.
An aeroplane leaves an airport and flies due north at a speed of 1,000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1,200 km per hour. How far apart will be the two planes after `1 1/2` hours?
Which of the following can be the sides of a right triangle?
1.5 cm, 2 cm, 2.5 cm
In the case of right-angled triangles, identify the right angles.
In the given figure, ∆ABC is an equilateral triangle of side 3 units. Find the coordinates of the other two vertices ?
In ∆ABC, seg AD ⊥ seg BC, DB = 3CD.
Prove that: 2AB2 = 2AC2 + BC2
O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.
In triangle PQR, angle Q = 90°, find: PR, if PQ = 8 cm and QR = 6 cm
In triangle PQR, angle Q = 90°, find: PQ, if PR = 34 cm and QR = 30 cm
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2(AD2 + CD2)
In a right-angled triangle PQR, right-angled at Q, S and T are points on PQ and QR respectively such as PT = SR = 13 cm, QT = 5 cm and PS = TR. Find the length of PQ and PS.
To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?
A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.
In figure, PQR is a right triangle right angled at Q and QS ⊥ PR. If PQ = 6 cm and PS = 4 cm, find QS, RS and QR.
The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is ______.
Two angles are said to be ______, if they have equal measures.
