Question

do it with explanation​

Answer 1

Answer:-

$\boxed{\red{\bf \therefore Perimeter = 48.58 \: units. }}$

Step-by-step explanation:

• Let the length of the rectangle be x units. And, the breadth of the rectangle be y units.

We know that,

• Area of rectangle = length * Breadth

= xy units².

It is given that,

• The area of the rectangle gets reduced by 9 sq units, if the length is reduced by 5 units and the breadth is increased by 3 units.

Thus,

$\implies \sf (x-5)(y+3)= xy - 9\\\\\implies \sf xy + 3x - 5y - 15 = xy - 9\\\\\implies \bf 3x - 5y = 15-9\\\\\implies \sf 3x - 5y = 6 \: \: \dots (i)$

Again, it is given that -

The area is increased by 63 sq units, if length is increased by 3 units and breadth is increased by 2 units .

So,

$\implies \sf (x+3)(y+2) = xy + 63\\\\\implies \sf xy + 2x + 3y + 6 = xy + 63 \\\\\implies \sf 2x + 3y = 63-6\\\\\implies \sf 2x + 3y = 57 \: \: \dots (ii)$

Multiplying equation (i) by 2 and equation (ii) by 3. We get ;-

$\sf \implies 6x - 10y = 12 \: \:\dots (iii) \\\\\implies \sf 6x + 9y = 171 \:\:\dots (iv)$

Subtracting equation (iii) from (iv),

$\implies \sf 6x - 10y - (6x + 9y)= 12 - 171\\\\\implies \sf 6x - 10y - 6x - 9y = - 159 \\\\\implies \sf - 19y = - 159 \\\\\implies \sf y = \frac{-159}{-19} \\\\\boxed{\red{\bf \therefore y = 8.36}}$

Now, substituting the value of y in (i),

$\implies \sf 3x-5y=6\\\\\implies \sf 3x - 5(8.36)=6\\\\\implies \sf 3x - 41.8 = 6 \\\\\implies \sf 3x = 6+41.8\\\\\implies \sf 3x = 47.8 \\\\\implies \sf x = \frac{47.8}{3} \\\\\boxed{\red{\bf \therefore x= 15.93}}$

Now, we know that :-

Perimeter of rectangle = 2 ( length + breadth )

                    = 2 ( x + y )

                    = 2 ( 15.93 + 8.36 )

                    = 2 ( 24.29 )

              = ⭐48.58 units. ⭐

• Hence, the perimeter of the given rectangle is 48.58 units.

________________________________________________

Answer 2

Answer:

Solution :-

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

Area = xy    

             

According to the question,                  

⇒ (x - 5) (y + 3) = xy - 9                  

⇒ 3x - 5y - 6 = 0 ... (i)                  

⇒ (x + 3) (y + 2) = xy + 67                  

⇒ 2x - 3y – 61 = 0 ... (ii)                  

By cross multiplication, we get                  

⇒ x/305 - (-18) = y/-12 -(-183) = 1/9 - (-10)                  

⇒ x/323 = y/171 = 1/19                  

⇒ x = 17, y = 9        

         

Length of the rectangle = 17 units.

Breadth of the rectangle = 9 units.

hope this helps you