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 the given figure, seg PS is the median of ∆PQR and PT ⊥ QR. Prove that,
PR2 = PS2 + QR × ST + `("QR"/2)^2`
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?
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 height of an equilateral triangle having side 2a.
Do sides 7 cm, 24 cm, 25 cm form a right angled triangle ? Give reason
Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.
A side of an isosceles right angled triangle is x. Find its hypotenuse.
In ∆ABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, Find AP.
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.
Choose the correct alternative:
Out of the following which is a Pythagorean triplet?
In ΔPQR, seg PM is a median, PM = 9 and PQ2 + PR2 = 290. Find the length of 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.
