Advertisements
Advertisements
Question
In ∆ABC, point M is the midpoint of side BC. If, AB2 + AC2 = 290 cm2, AM = 8 cm, find BC.
Advertisements
Solution
In ∆ABC, point M is the midpoint of side BC.
AB2 + AC2 = 2AM2 + 2BM2 ...[by Apollonius theorem]
290 = 2 (8)2 + 2BM2
290 = 2 (64) + 2BM2
290 = 128 + 2BM2
2BM2 = 290 - 128
2BM2 = 162
BM2 = 81
BM = `sqrt81`
BM = 9 cm
Point M is the midpoint of BC
∴ BC = 2BM = 2 × 9
∴ BC = 18 cm.
RELATED QUESTIONS
Adjacent sides of a parallelogram are 11 cm and 17 cm. If the length of one of its diagonal is 26 cm, find the length of the other.
Find the perimeter of a square if its diagonal is `10sqrt2` cm:
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.
In ∆ABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, Find AP.
Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.
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.
Choose the correct alternative:
Out of given triplets, which is not a Pythagoras triplet?
Height and base of a right angled triangle are 24 cm and 18 cm. Find the length of its hypotenus?
"The diagonals bisect each other at right angles." In which of the following quadrilaterals is the given property observed?
Which of the following figure is formed by joining the mid-points of the adjacent sides of a square?
