The area of a rectangle is $6 x^{2} - 4 x y - 10 y^{2}$ square unit and its length is $2 x + 2 y$ unit. Find its breadth.

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Solution

Let the breadth of the rectangle be $b .$

Length $\times$ Breadth $=$ Area
$\Rightarrow (2 x + 2 y) \times b = 6 x^{2} - 4 x y - 10 y^{2}$
$\Rightarrow b = (6 x^{2} - 4 x y - 10 y^{2}) \div (2 x + 2 y)$
$\Rightarrow b = 3 x - 5 y$ [Refer the given image]

Hence, the breadth of the rectangle is equal to $3 x - 5 y$ units.

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The area of a rectangle gets reduced by 9 square units. if its length is reduced by 5 units and breadth is increased by 3 units. However, if the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Let the length of the rectangle = x units and its breadth = y units

According to first condition :
$(x - 5) (y + 3) = x y - 9$ and

According to second condition:
$(x + 3) (y + 2) = x y + 67$

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9

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5

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Q. If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 8 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of the rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.

Q. The area of a rectangle gets reduced by

9

square units, if its 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.

The area of a rectangle gets reduced by $9$ square units if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and breadth by $2$ units, the area increases by $67$ square units. Find the dimensions of the rectangle.

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The area of a rectangle is 6x2−4xy−10y2 square unit and its length is 2x+2y unit. Find its breadth.

Let the breadth of the rectangle be b.Length × Breadth = Area⇒(2x+2y)×b=6x2−4xy−10y2⇒b=(6x2−4xy−10y2)÷(2x+2y)⇒b=3x−5y [Refer the given image]Hence, the breadth of the rectangle is equal to 3x−5y units.

The area of a rectangle is $6 x^{2} - 4 x y - 10 y^{2}$ square unit and its length is $2 x + 2 y$ unit. Find its breadth.