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`
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:
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
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.
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?
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?
Height and base of a right angled triangle are 24 cm and 18 cm. Find the length of its hypotenus?
Which of the following figure is formed by joining the mid-points of the adjacent sides of a square?
