Question

the diagonals oy a parallelogram PQRS are along the lines x+3y=4 and 6x-2y=7
then PQRS must be a ?

Answer 1

*of

Answer 2

@rational please help

Answer 3

@ikram002p may u please help me

Answer 4

Hint : the given lines are perpendicular

Answer 5

i know that

Answer 6

Next use this :

A parallelogram with perpendicular diagonals is called a "rhombus"

Answer 7

oh
so its not square?

Answer 8

@rational

Answer 9

it has to be a rhombus i think..

Answer 10

hmm

Answer 11

yeah it can be square as well

Answer 12

it has to be a rhombus

Answer 13

ikky took a ruler to her screen to draw out those lines :P Hahaha jk!

Answer 14

so which is right

Answer 15

jhanny lol xD

Answer 16

not all rhombuses are squares

so saying "it has to be a square" is incorrect

Answer 17

i said it might be also square xD

Answer 18

it can be a cube also if you stretch it and take it to 3D (some sarcasm)

Answer 19

:P

Answer 20

lol
this souns interesting @rational

Answer 21

this is why the one who ask should be careful :P
any imagination answer can be correct

Answer 22

nope, the only possible answer is "rhombus"

Answer 23

but yeah according to the definition of rhombus its the parallelogram of perpendicular diagonals, and square belongs to rhombus family so hmmm

Answer 24

well the ans is rhombus but i just need a proof for that :)

Answer 25

consider a quadratic equation ax^2 + bx + c = 0

and it is given that b^2-4ac > 0

what can you say about the nature of roots ?

Answer 26

oh @rvc all u need is to find the slope of both lines to show they are perpendicular :)

Answer 27

options :

1) roots must be integers
2) roots must be rationsl
3) roots must be perfect squares
4) roots must be mangoes

Answer 28

okay

then

Answer 29

1)

Answer 30

the answer is actually NONE OF THEM.

Answer 31

because `b^2-4ac > 0` is only a sufficient condition for "real roots"

Answer 32

ohh
yes

Answer 33

hahaha ok got it xDDDDDDD
if there is other options like
they might be integer
they might be rational
they might be morons
any thing fits :P

Answer 34

ugh, the point im trying is to convince us that

none of them fit

Answer 35

i know, i totally agree when the student still in school
i just wanna see what @rvc is about to say

Answer 36

OK \[b^2 - 4ac \ge 0\implies \text{roots are real}\]
end of story.

Answer 37

\[b^2 - 4ac \ge 0\implies \text{roots are integers}\]

is incorrect as it doesn't hold always.

Answer 38

rectangle,rhombus,square,cyclic quadrilateral

Answer 39

\[\text{Sheela's dress became wet} \implies \text{It rained}\]

the implication is wrong because there might be other reasons for Sheela to become wet

Answer 40

sheela is my math teacher's name
lol

Answer 41

\[\text{perpendicular diagonals} \implies \text{parallelogram is square}\]


the implication is wrong because there might be other possibilities for parallelogram other than square.

Answer 42

xD then dont tell her husbend were using her in question @rvc xD

Answer 43

However below implication holds

\[\text{perpendicular diagonals} \implies \text{parallelogram is rhombus}\]

Answer 44

ok i agree

Answer 45

lol @ikram002p

Answer 46

well im not convinced its a rhombus

Answer 47

what u are thinking it is ?

Answer 48

im confused

Answer 49

you may google for a proof of

"A parallelogram with perpendicular diagonals is a rhombus"

Answer 50

ok so ur agree both lines are perpendicular diagonals ?