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
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.
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
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.
PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
In the given figure, ∆ABC is an equilateral triangle of side 3 units. Find the coordinates of the other two vertices ?
Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)
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.
In the following figure, OP, OQ, and OR are drawn perpendiculars to the sides BC, CA and AB respectively of triangle ABC.
Prove that: AR2 + BP2 + CQ2 = AQ2 + CP2 + BR2
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)
In the given figure, BL and CM are medians of a ∆ABC right-angled at A. Prove that 4 (BL2 + CM2) = 5 BC2.
A ladder, 6.5 m long, rests against a vertical wall. If the foot of the ladder is 2.5 m from the foot of the wall, find up to how much height does the ladder reach?
In the figure below, find the value of 'x'.
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: AB2 + AC2 = 2(AD2 + CD2)
In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.
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?
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 a right-angled triangle ABC, if angle B = 90°, then which of the following is true?
If the areas of two circles are the same, they are congruent.
