Advertisements
Advertisements
Question
In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.
Solution
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`
RELATED QUESTIONS
ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2
Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?
Which of the following can be the sides of a right triangle?
2 cm, 2 cm, 5 cm
In the case of right-angled triangles, identify the right angles.
In the given figure, ∆ABC is an equilateral triangle of side 3 units. Find the coordinates of the other two vertices ?
In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2.
In the given figure, BL and CM are medians of a ∆ABC right-angled at A. Prove that 4 (BL2 + CM2) = 5 BC2.
Triangle PQR is right-angled at vertex R. Calculate the length of PR, if: PQ = 34 cm and QR = 33.6 cm.
The sides of a certain triangle is given below. Find, which of them is right-triangle
6 m, 9 m, and 13 m
In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.
In the right-angled ∆PQR, ∠ P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.
Find the Pythagorean triplet from among the following set of numbers.
4, 5, 6
Find the Pythagorean triplet from among the following set of numbers.
9, 40, 41
The sides of the triangle are given below. Find out which one is the right-angled triangle?
1.5, 1.6, 1.7
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that : 9(AQ2 + BP2) = 13AB2
Determine whether the triangle whose lengths of sides are 3 cm, 4 cm, 5 cm is a right-angled triangle.
The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ = 9 cm, then AB equals ______.
A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.
The longest side of a right angled triangle is called its ______.
Two angles are said to be ______, if they have equal measures.
