Advertisements
Advertisements
प्रश्न
If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.
उत्तर
The sides of the triangle are 6 cm, 8 cm and 10 cm.
The longest side is 10 cm.
(10)2 = 100 ….(i)
Now, the sum of the squares of the other two sides will be,
(6)2 + (8)2 = 36 + 64 = 100 ….(ii)
(10)2 = (6)2 + (8)2 ….. from (i) and (ii)
By the converse of Pythagoras theorem:
The given sides form a right angled triangle.
APPEARS IN
संबंधित प्रश्न
In triangle ABC, ∠C=90°. Let BC= a, CA= b, AB= c and let 'p' be the length of the perpendicular from 'C' on AB, prove that:
1. cp = ab
2. `1/p^2=1/a^2+1/b^2`
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals
In an equilateral triangle ABC, D is a point on side BC such that BD = `1/3BC` . Prove that 9 AD2 = 7 AB2
Prove that the points A(0, −1), B(−2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)
Identify, with reason, if the following is a Pythagorean triplet.
(4, 9, 12)
Some question and their alternative answer are given. Select the correct alternative.
If a, b, and c are sides of a triangle and a2 + b2 = c2, name the type of triangle.
In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:
4(BL2 + CM2) = 5 BC2
In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.
The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD = ∠BCD = 90o. Calculate the length of AB.
If P and Q are the points on side CA and CB respectively of ΔABC, right angled at C, prove that (AQ2 + BP2 ) = (AB2 + PQ2)
Prove that `(sin θ + cosec θ)^2 + (cos θ + sec θ)^2 = 7 + tan^2 θ + cot^2 θ`.
Triangle XYZ is right-angled at vertex Z. Calculate the length of YZ, if XY = 13 cm and XZ = 12 cm.
Find the Pythagorean triplet from among the following set of numbers.
9, 40, 41
A ladder 25m long reaches a window of a building 20m above the ground. Determine the distance of the foot of the ladder from the building.
An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height
In the figure, find AR
In an equilateral triangle PQR, prove that PS2 = 3(QS)2.
A right-angled triangle may have all sides equal.
Points A and B are on the opposite edges of a pond as shown in figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.
