Advertisements
Advertisements
Question
Identify, with reason, if the following is a Pythagorean triplet.
(24, 70, 74)
Advertisements
Solution
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
RELATED QUESTIONS
The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right traingle ,right-angled at B. Find the values of p.
In figure, ∠B of ∆ABC is an acute angle and AD ⊥ BC, prove that AC2 = AB2 + BC2 – 2BC × BD
P and Q are the mid-points of the sides CA and CB respectively of a ∆ABC, right angled at C. Prove that:
`(i) 4AQ^2 = 4AC^2 + BC^2`
`(ii) 4BP^2 = 4BC^2 + AC^2`
`(iii) (4AQ^2 + BP^2 ) = 5AB^2`
Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 13 cm, 12 cm, 5 cm
Identify, with reason, if the following is a Pythagorean triplet.
(11, 60, 61)
In triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm2.
Find x.
ABC is a triangle, right-angled at B. M is a point on BC.
Prove that: AM2 + BC2 = AC2 + BM2
In the following Figure ∠ACB= 90° and CD ⊥ AB, prove that CD2 = BD × AD
In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.
In ΔABC, AD is perpendicular to BC. Prove that: AB2 + CD2 = AC2 + BD2
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 = AD2 + BC x DE + `(1)/(4)"BC"^2`
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2(AD2 + CD2)
AD is perpendicular to the side BC of an equilateral ΔABC. Prove that 4AD2 = 3AB2.
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 a right angled triangle, if length of hypotenuse is 25 cm and height is 7 cm, then what is the length of its base?
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 the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:
(i) `"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`
(ii) `"AB"^2 = "AD"^2 - "BC"."DM" + (("BC")/2)^2`
(iii) `"AC"^2 + "AB"^2 = 2"AD"^2 + 1/2"BC"^2`
Two rectangles are congruent, if they have same ______ and ______.
Points A and B are on the opposite edges of a pond as shown in the following figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.
