Advertisements
Advertisements
Question
In ΔPQR, seg PM is the median. If PM = 9, PQ2 + PR2 = 290, Find QR.
Solution
PM = 9 ; PQ2 + PR2 = 290
To find QR
∵ PM is the median of QR.
So, by apollonius theorem,
PQ2 + PR2 = 2 PM2 + 2 QM2
290 = 2(9)2 + 2(QM)2
290 = 2 [81 + (QM)2]
145 = 81 + QM2
QM2 = 145 - 81
QM2 = 64
QM = 8
QM = 2 × QM = 2 × 8 = 16 units
APPEARS IN
RELATED QUESTIONS
Out of the following, which is the Pythagorean triplet?
Some question and their alternative answer are given. Select the correct alternative.
Find perimeter of a square if its diagonal is \[10\sqrt{2}\]
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
Find the height of an equilateral triangle having side 2a.
A side of an isosceles right angled triangle is x. Find its hypotenuse.
In ∆RST, ∠S = 90°, ∠T = 30°, RT = 12 cm then find RS and ST.
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.
Seg PM is a median of ∆PQR. If PQ = 40, PR = 42 and PM = 29, find QR.
If hypotenuse of a right angled triangle is 5 cm, find the radius of
the circle passing through all vertices of the triangle.
Choose the correct alternative:
Out of the following which is a Pythagorean triplet?
Choose the correct alternative:
Out of given triplets, which is not a Pythagoras triplet?
Choose the correct alternative:
Out of all numbers from given dates, which is a Pythagoras triplet?
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.
