Advertisements
Advertisements
प्रश्न
Identify, with reason, if the following is a Pythagorean triplet.
(24, 70, 74)
Advertisements
उत्तर
In the triplet (24, 70, 74),
242 = 576, 702 = 4900, 742 = 5476 and 576 + 4900 = 5476
The square of the largest number is equal to the sum of the squares of the other two numbers.
∴ (24, 70, 74) is a pythagorean triplet.
APPEARS IN
संबंधित प्रश्न
ABCD is a rectangle whose three vertices are B (4, 0), C(4, 3) and D(0,3). The length of one of its diagonals is
(A) 5
(B) 4
(C) 3
(D) 25
A man goes 10 m due east and then 24 m due north. Find the distance from the starting point
From a point O in the interior of a ∆ABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove
that :
`(i) AF^2 + BD^2 + CE^2 = OA^2 + OB^2 + OC^2 – OD^2 – OE^2 – OF^2`
`(ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2`
In the following figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that
(i) OA2 + OB2 + OC2 − OD2 − OE2 − OF2 = AF2 + BD2 + CE2
(ii) AF2 + BD2 + CE2 = AE2 + CD2 + BF2
A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.
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.
Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.
In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS2 + TQ2 = TP2 + TR2 (As shown in the figure, draw seg AB || side SR and A-T-B)
Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was \[15\sqrt{2}\]
km. Find their speed per hour.
In the following figure, AD is perpendicular to BC and D divides BC in the ratio 1: 3.
Prove that : 2AC2 = 2AB2 + BC2
Find the value of (sin2 33 + sin2 57°)
Triangle PQR is right-angled at vertex R. Calculate the length of PR, if: PQ = 34 cm and QR = 33.6 cm.
Find the Pythagorean triplet from among the following set of numbers.
3, 4, 5
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 12, 15
The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?
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.
In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.
Two squares having same perimeter are congruent.
