Advertisements
Advertisements
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.
Advertisements
उत्तर
Let □PQRS be a parallelogram.
Then, PQ = 17 cm, QR = 11 cm and diagonal PR = 26 cm The diagonals of a parallelogram bisect each other. Point M is the point of intersection of diagonals PR and QS.
`therefore PM=MR=1/2PR=1/2xx26`
`therefore PM=MR=13 cm ......(1)`
`QM=1/2QS`
`thereforeQS=2QM......(2)`
In ΔPQR, QM is the median.
`PQ^2+QR^2=2PM^2+2QM^2` .......(By Apollonius theorem)
`(17)^2+(11)^2=2(13)^2+2QM^2`
`therefore 289+121=2(169)+2QM^2`
`therefore 410=2(169)+2QM^2`
Diving by 2, we get
`205 =169 + QM^2`
`therefore QM^2= 205 -169=36`
`therefore QM=6`
`therefore QS=2QM=2xx6=12cm`
Thus, the length of the other diagonal is 12 cm.
APPEARS IN
संबंधित प्रश्न
In the given figure, seg PS is the median of ∆PQR and PT ⊥ QR. Prove that,
PR2 = PS2 + QR × ST + `("QR"/2)^2`
Find the perimeter of a square if its diagonal is `10sqrt2` cm:
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.
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.
In ∆RST, ∠S = 90°, ∠T = 30°, RT = 12 cm, then find RS and ST.
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 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.
In ΔABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, then find the length of AP.
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 hypotenuse?
"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?
