English, asked by chettanprince, 6 months ago

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

Answered by gaurvendrasingh95
1

Explanation:

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Answered by mohammedthoufeeq2005
0

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

                                                                                             

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