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`
In ∆ABC, point M is the midpoint of side BC. If, AB2 + AC2 = 290 cm2, AM = 8 cm, find BC.
Out of the following, which is the Pythagorean triplet?
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:
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.
Do sides 7 cm, 24 cm, 25 cm form a right angled triangle ? Give reason
In ∆RST, ∠S = 90°, ∠T = 30°, RT = 12 cm, then find RS and ST.
In ∆ABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, Find AP.
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.
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?
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.
