Advertisements
Advertisements
Question
In ΔPQR, seg PM is the median. If PM = 9, PQ2 + PR2 = 290, Find QR.
Advertisements
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
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.
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?
Find the perimeter of a square if its diagonal is `10sqrt2` cm:
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.
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.
Seg AM is a median of ∆ABC. If AB = 22, AC = 34, BC = 24, find AM
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?
In ΔABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, then find the length of AP.
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?
"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?
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.
