Advertisements
Advertisements
प्रश्न
Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.
Advertisements
उत्तर
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.
संबंधित प्रश्न
Two towers of heights 10 m and 30 m stand on a plane ground. If the distance between their feet is 15 m, find the distance between their tops
In Fig., ∆ABC is an obtuse triangle, obtuse angled at B. If AD ⊥ CB, prove that AC2 = AB2 + BC2 + 2BC × BD
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?
Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.
In an isosceles triangle, length of the congruent sides is 13 cm and its base is 10 cm. Find the distance between the vertex opposite the base and the centroid.
Digonals of parallelogram WXYZ intersect at point O. If OY =5, find WY.
In triangle ABC, AB = AC and BD is perpendicular to AC.
Prove that: BD2 − CD2 = 2CD × AD
In a quadrilateral ABCD, ∠B = 90° and ∠D = 90°.
Prove that: 2AC2 - AB2 = BC2 + CD2 + DA2
In the given figure, BL and CM are medians of a ∆ABC right-angled at A. Prove that 4 (BL2 + CM2) = 5 BC2.
The sides of a certain triangle is given below. Find, which of them is right-triangle
6 m, 9 m, and 13 m
A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.
From the given figure, find the length of hypotenuse AC and the perimeter of ∆ABC.
Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.
Two poles of height 9m and 14m stand on a plane ground. If the distance between their 12m, find the distance between their tops.
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9BP2 = 9BC2 + 4AC2
∆ABC is right-angled at C. If AC = 5 cm and BC = 12 cm. find the length of AB.
A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?
Find the unknown side in the following triangles
From the given figure, in ∆ABQ, if AQ = 8 cm, then AB =?
If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent.
