Question

the area of rectangle is equals with the area of square which is formed the rectangle length is decreased by 4cm and breadth is increased by 3cm.then find the perimeter of rectangle?​

Answer 1

Step-by-step explanation:

50

If 'L' be the length and 'B' be the breadth of the rectangle, then decreasing the length and increasing the breadth we get,

L=L-4; B=B+3

So, it became Square. L-4=B+3 or L-B=7.......(1)

Area of a Square= (L-4)^2= LxB or L^2 +16 -8L= LxB

or L^2-LxB +16 -8L=0 or L(L-B)+16 -8L=0

or L(7) +16 -8L=0.....from equtn (1)

or 7L-8L +16=0

or L= 16

then B=9

Perimeter of Rectangle 2(L+B)=50

144..

by the given question we can form 2 eqs

let 'L' be the length n 'B' be the breadth

3L-4B=12

L-B=7

by solving we get L=16,B=9

so the perimeter is 16*9=144

(NOTE:we can also cross check..in the question it was given dat we length decreased by 4 and breadth increased by 3 then it forms a SQUARE

L=16-4=12 B=9+3=12)

Answer 2

Answer:

50 cm

Step-by-step explanation:

According to the question,

              Area of rectangle=Area of square which is formed by altering the measurements of rectangle

Let the length be l and breadth be b

⇒ Since (l-4) and (b+3) are the sides of a square, we can equate them.

⇒ ∴ l-4 = b+3

⇒ l-b = 7 --------------- (I)

Now we know that Area of rectangle=Area of square

⇒ l×b = (l-4)×(b+3)

⇒ lb = lb+3l-4b-12

⇒ 3l-4b = 12 --------------(II)

Multiplying 3 in eqn. (I) and subtracting eqn (II) from (I)

⇒ 3l-3b = 21   and 3l-4b = 12

⇒ 3l-3b = 21

  -3l+4b = -12

⇒ b = 9 cm   AND l = 16 cm

∴ Perimeter of rectangle = 2(l+b)

                                         = 2(9+16)

                                         = 2×25

                                         = 50 cm    ←ANSWER

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