The length of a rectangle is 1 metre more than its breadth. Its area is 3 3/4 square metres. What are its length and breadth ?
Answers
Explanation:
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Answer :Length = x
Breadth = y
x = y + 1; x – y = 1
Area of the rectangle= xy = 3 3/4 = 15/4
15/4 = (y+1)*y
15/4 =y^2 + y
15 = 4 (y^2+ y)
15 = 4y^2+ 4y
4y^2+4y-15 = 0
4y^2-6y+10y-15 = 0
(4y^2-6y)+(10y-15)=0
2y(2y-3)+5 (2y-3)=0
2y-3=0 or 2y+5=0
2y= 3 or 2y=-5
y=3/2 or y= -5/2
hence rectangle's side cannot be negative
y=3/2 = 1.5
x= y+1
x= 1.5+ 1 = 2.5
(answer is in the last line)
Deep level Explanation:
let length be x and breadth be
length = breadth + 1, length-breadth = 1
derive it and you get xy =3 3/4 4multiplied by 3 + 3 that 'll give you 15/4
and then put the value breadth + 1 which is y+1 in the x's place
then we have to multiply the (y+1) * y
y^2 + 1y = one is not needed so = y^2 + y
in the LHS the denominator of 15/4 ,4 we have to put it on the RHS
which will get changed and turn to multiplication
it will be like this 15 x 4(y^2+y) then we have to multiply both 'y' with 4
then take the 15 to the RHS it will change to subtraction 4y^2+4y-15 = 0
in order to find the value of 'y' we have to use splitting the middle terms
the middle term 4y^2+'4y'-15 = 0 what we are doing is splitting the 4y with some random numbers its sum needs to be 4 and its product needs to be -60
you guys will be thinking how did -15 came well we are taking the co efficient of y^2 which is 4 and multiplying it by -15 which is a constant and
we have to find these random numbers so 6 and 10 are there (it's sum will be 16 which is 10+6 and its product will be 60) but we need 4 so we can put minus to the 6 which will be -6 and 10 = sum = 4 and product will be -60
so the two conditions are solved
we can easily split +4y like 4y^2-6y+10y-15 = 0
and then we have group them into two (4y^2-6y)+(10y-15)=0
after that we have to take a common factor which will be 2y, 2y and 5 it will be like this 2y(2y-3)+5 (2y-3)=0 again we have to group them "ahgg!! fraustrating calm down its eazy only"
(2y+5) (2y-3) = 0 this mentions that 2y+5 = 0, 2y-3 = 0
then we have to find the value of y from these two in first equation and second equation
2y-3=0 '-3' (minus three) goes to the RHS and turn to +3 that means it turns to 2y=3 and take the 2 divide it by three y= 3/2 actually dont have to divide it so simply put y=3/2 just like this one we're gonna find for the other one too
2y+5=0 be careful it was plus on the LHS side so when it goes to the RHS side it'll turn to -5
so 2y=-5 the two was multiplication on the LHS side when it goes to RHS it turns to division y= -5/2 so one thing about maths is that it'll make you suffer to get an answer so keep trying again
this is the part we took y as breadth so "Polynomials cannot contain negative measurment" so we have to sacrifice -5/2 ~~ಥ_ಥ
so y = 3/2 which is 1.5
so in first equation we found that length = to one more than breadth here's your equation x=y+1 so we already got y we gotta find x so x= 1.5 +1 = to 2.5
FINALLY GUYS HERE'S YOUR FINAL ANSWER
LENGTH = 2.5
BREADTH = 1.5