Math, asked by vandsharma1977, 1 month ago

The area of rectangle gets reduced by 9 square units, if it's length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units , the area increases by 67 square units. Find the dimensions of the rectangle. [obtain the algebraic equations and solve them by cross multiplication method]​

Answers

Answered by neeleshpravin
0

Answer:

the length of the rectangle = 17 units.

The breadth of the rectangle = 9 units

Step-by-step explanation:

Let the length and breadth of the rectangle be x unit and y unit.

Now the 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

Therefore, the length of the rectangle = 17 units.

The breadth of the rectangle = 9 units.

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