Advertisements
Advertisements
प्रश्न
If the sides of the triangle are in the ratio 1: `sqrt2`: 1, show that is a right-angled triangle.
Advertisements
उत्तर
Let, the sides of the triangle be, x: `sqrt2`x and x.
AB2 + BC2 = x2 +x2 = 2x2
AC2 = `(sqrt2 x)^2` = 2x2
AB2 + BC2 = AC2
Conversely, if in any triangle, the square on the largest side of the triangle is equal to the sum of the squares on remaining two sides, then the triangle is a right-angled triangle and the angle opposite to the largest side is a right-angle.
Therefore, Δ ABC is a right-angled triangle.
APPEARS IN
संबंधित प्रश्न
The perpendicular from A on side BC of a Δ ABC intersects BC at D such that DB = 3CD . Prove that 2AB2 = 2AC2 + BC2.
In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2 + 2BC.BD.
In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:
`"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`
Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.
Prove that the points A(0, −1), B(−2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
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 a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)
A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.
In triangle ABC, ∠B = 90o and D is the mid-point of BC.
Prove that: AC2 = AD2 + 3CD2.
Find the side of the square whose diagonal is `16sqrt(2)` cm.
Triangle XYZ is right-angled at vertex Z. Calculate the length of YZ, if XY = 13 cm and XZ = 12 cm.
In triangle PQR, angle Q = 90°, find: PQ, if PR = 34 cm and QR = 30 cm
Find the Pythagorean triplet from among the following set of numbers.
4, 7, 8
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED
In the given figure. PQ = PS, P =R = 90°. RS = 20 cm and QR = 21 cm. Find the length of PQ correct to two decimal places.
If in a ΔPQR, PR2 = PQ2 + QR2, then the right angle of ∆PQR is at the vertex ________
Is the triangle with sides 25 cm, 5 cm and 24 cm a right triangle? Give reasons for your answer.
Two trees 7 m and 4 m high stand upright on a ground. If their bases (roots) are 4 m apart, then the distance between their tops is ______.
In a right-angled triangle ABC, if angle B = 90°, then which of the following is true?
