Advertisements
Advertisements
प्रश्न
In ΔPQR, seg PM is the median. If PM = 9, PQ2 + PR2 = 290, Find QR.
Advertisements
उत्तर
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
संबंधित प्रश्न
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.
In the given figure, seg PS is the median of ∆PQR and PT ⊥ QR. Prove that,
PR2 = PS2 + QR × ST + `("QR"/2)^2`
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?
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.
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.
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.
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 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?
