Advertisements
Advertisements
Question
In ΔABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, then find the length of AP.
Advertisements
Solution
We know, By Apollonius theorem
In ΔABC,
if P is the midpoint of side BC, then AB2 + AC2 = 2AP2 + 2BP 2
Given that, AP is median i.e. P is the mid-point of BC
BP = CP = `1/2"BC" = 9`
And BC = 18 cm
and AB2 + AC2 = 260
⇒ 260 = 2AP2 + 2(9)2
⇒ 260 = 2AP2 + 162
⇒ 98 = 2AP2
⇒ AP2 = 49
⇒ AP = 7 units
APPEARS IN
RELATED QUESTIONS
In ∆ABC, point M is the midpoint of side BC. If, AB2 + AC2 = 290 cm2, AM = 8 cm, find BC.
Some question and their alternative answer are given.
In a right-angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?
Some question and their alternative answer are given. Select the correct alternative.
Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.
Height and base of a right angled triangle are 24 cm and 18 cm find the length of its hypotenuse
Some question and their alternative answer are given. Select the correct alternative.
In ∆ABC, AB = \[6\sqrt{3}\] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.
Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.
Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.
Sum of the squares of adjacent sides of a parallelogram is 130 sq.cm and length of one of its diagonals is 14 cm. Find the length of the other diagonal.
If hypotenuse of a right angled triangle is 5 cm, find the radius of
the circle passing through all vertices of the triangle.
In ΔPQR, seg PM is a median, PM = 9 and PQ2 + PR2 = 290. Find the length of QR.
In ΔPQR, seg PM is the median. If PM = 9, PQ2 + PR2 = 290, Find QR.
Out of given triplets, which is not a Pythagoras triplet?
Out of given triplets, which is not a Pythagoras triplet?
Out of all numbers from given dates, which is a Pythagoras triplet?
Height and base of a right angled triangle are 24 cm and 18 cm. Find the length of its hypotenuse?
Which of the following figure is formed by joining the mid-points of the adjacent sides of a square?
In the given figure, triangle ABC is a right-angled at B. D is the mid-point of side BC. Prove that AC2 = 4AD2 – 3AB2.
