Q. 124.5( 14 Votes )

Sum of the square

Answer :

Let ABCD be a parallelogram, with AB = CD ; AB || CD and BC = AD ; BC || AD.


Construct AE CD and extend CD to F such that, BF CF.



Given: sum of squares of adjacent side = 130


CD2 + BC2 = 130 and


Length of one diagonal = 14 cm [let it be AC]


To Find: length of the other diagonal, BD


In ΔAED and ΔBCF


AE = BF [Distance between two parallel lines i.e. AB and CD]


AD = BC [opposite sides of a parallelogram are equal]


AED = BFC [Both 90°]


ΔAED ΔBCF [By Right Angle - Hypotenuse - Side Criteria]


DE = CF [Corresponding sides of congruent triangles are equal] [1]


In ΔBFD, By Pythagoras theorem i.e.


(Hypotenuse)2 = (base)2 + (Perpendicular)2


BD2 = DF2 + BF2


BD2 = (CD + CF)2 + BF2 [2]


In ΔAEC, By Pythagoras theorem


AC2 = AE2 + CE2


AC2 = AE2 + (CD - AE)2


AC2 = BF2 + (CD - CF)2 [As, AE = BF and CF = AE] [2]


In ΔBCF, By Pythagoras theorem,


BC2 = BF2 + CF2


BF2 = BC2 - CF2 [3]


Adding [2] and [3]


BD2 + AC2 = 2BF2 + (CD + CF)2 + (CD - CF)2


BD2 + AC2= 2BC2 - 2CF2 + CD2 + CF2 + 2CD.CF + CD2 + CF2 - 2CD.CF


BD2 + AC2 = 2BC2 + 2CD2


BD2 + 142 = 2(130)


BD2 + 196 = 260 [Using given data]


BD2 = 64


BD = 8 cm


Hence, length of other diagonal is 8 cm.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Prove that the suMHB - Mathematics Part-2

Sum of the squareMHB - Mathematics Part-2

From the informatMHB - Mathematics Part-2

In the figure 2.3MHB - Mathematics Part-2

Some questions anMHB - Mathematics Part-2

In figure 2.30, pMHB - Mathematics Part-2

Pranali and PrasaMHB - Mathematics Part-2

Find the side andMHB - Mathematics Part-2

In the figure 2.2MHB - Mathematics Part-2

Find the diagonalMHB - Mathematics Part-2