6. If the length of the rectangle is reduced by
3 unints & breadth is in are aseet
square units we increase the lengan
bys units & the breadth by 3 units
units. Find the climension of the rectangle
Answers
Answer:
Let their present ages be x and 20−x yrs respectively.
Four years ago, their ages would be (x-4) and (16-x) yrs respectively.
(x−4)(16−x)=48
16x−x
2
−64+4x=48
x
2
−20x+112=0
b
2
−4ac=−48
Since the discriminant <0, the roots would be imaginary.
Hence, such a situation is not possible.
Answer:
area of the rectangle, A=xy.
Now, According to the statement given in the question, we have
The length is reduced by 5 units and the breadth is increased by 3 units. And the area has decreased by 9 units.
So , the new length will be =x−5
So , the new breadth will be =y+3
New area = xy−9
So, the new the relation will be
(x−5)(y+3)=xy−9⇒3x−5y−6=0→eqn(1)
Also, when the length is increased by 3 units and the breadth is increased by 2 units, then the area Is increased by 67 units.
New length = x+3
New breadth will be =y+2
New area = xy+67
So, the new the relation will be
(x+3)(y+2)=xy+67⇒2x+3y−61=0→eqn(2)
We know, cross – multiplication method
a1x+b1y+c1=0a2x+b2y+c2=0
Then they can be solved by using the relation
xb1c2−b2c1=ya2c1−c2a1=1a1b2−a2b1x=b1c2−b2c1a1b2−a2b1,y=a2c1−c2a1a1b2−a2b1
⇒x305−(−18)=y−12−(−183)=19−(−10)⇒x323=y171=119⇒x=17,y=9