Advertisements
Advertisements
प्रश्न
Find the Pythagorean triplet from among the following set of numbers.
3, 4, 5
Advertisements
उत्तर
It is known that, if in a triplet of natural numbers, the square of the biggest number is equal to the sum of the squares of the other two numbers, then the three numbers form a Pythagorean triplet.
The given set of numbers is (3, 4, 5).
The biggest number among the given set is 5.
52 = 25; 42 = 16; 32 = 9
Now, 16 + 9 = 25
∴ 42 + 32 = 52
Thus, (3, 4, 5) form a Pythagorean triplet.
संबंधित प्रश्न
A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:
4(BL2 + CM2) = 5 BC2
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m;
find the distance between their tips.
M andN are the mid-points of the sides QR and PQ respectively of a PQR, right-angled at Q.
Prove that:
(i) PM2 + RN2 = 5 MN2
(ii) 4 PM2 = 4 PQ2 + QR2
(iii) 4 RN2 = PQ2 + 4 QR2(iv) 4 (PM2 + RN2) = 5 PR2
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 the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.
Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?
In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is ______.
For going to a city B from city A, there is a route via city C such that AC ⊥ CB, AC = 2x km and CB = 2(x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.
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.
