Advertisements
Advertisements
प्रश्न
In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.
Advertisements
उत्तर
Let CD be the median drawn from the vertex C to side AB.
`"BD" = 1/2 × "AB"` ...(D is the midpoint of AB)
∴ BD = `1/2 × 10`
∴ BD = 5 units
In ∆ABC,
seg CD is the median. ...(Given)
By Apollonius theorem,
∴ AC2 + BC2 = 2CD2 + 2BD2
∴ 72 + 92 = 2CD2 + 2(5)2
∴ 49 + 81 = 2CD2 + 2 × 25
∴ 130 = 2CD2 + 50
∴ 2CD2 = 130 − 50
∴ CD2 = `80/2`
संबंधित प्रश्न
In a right triangle ABC, right-angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle (in cm) is ______.
In the given figure, ∆ABC is an obtuse triangle, obtuse-angled at B. If AD ⊥ CB (produced) prove that AC2 = AB2 + BC2 + 2BC · BD.
In figure, ∠B of ∆ABC is an acute angle and AD ⊥ BC, prove that AC2 = AB2 + BC2 – 2BC × BD
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 sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.
ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.
Find the length diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2.
A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.
In triangle ABC, given below, AB = 8 cm, BC = 6 cm and AC = 3 cm. Calculate the length of OC.
In an isosceles triangle ABC; AB = AC and D is the point on BC produced.
Prove that: AD2 = AC2 + BD.CD.
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 figure below, find the value of 'x'.
The sides of the triangle are given below. Find out which one is the right-angled triangle?
8, 15, 17
A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.
In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.
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.
In a square PQRS of side 5 cm, A, B, C and D are points on sides PQ, QR, RS and SP respectively such as PA = PD = RB = RC = 2 cm. Prove that ABCD is a rectangle. Also, find the area and perimeter of the rectangle.
A right-angled triangle may have all sides equal.
