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If the length of a rectangle is decreased by 6 cm and the width is increased by 3 cm, the result will be a square, the area of which will be 27 cm^2 smaller than the area of the rectangle. Find the area of the rectangle.

Respuesta :

Wahmmy

Answer:

252 centimeters squared is the answer.

asuwafohjames

The area of the rectangle is 252 cm².

What is a rectangle?

A rectangle is a plane shape that has pair of opposite sides and angles equal

To calculate the area of a rectangle, we use the formula below.

Formula:

Area of a rectangle(A) = Length(L)×Width(W).............. Equation 1

⇒ Let the length of the rectangle be x and the width of the rectangle be y.

If the length is decreased by 6 cm

  • new length = (x-6) cm

And if the width is increased by 3 cm

  • new width = (y+3) cm

Since the new length and the new width form a square,

Note: In a square, all sides are equal

  • (x-6) = (y+3)
  • x = y+9...................... Equation 2

Also, The area of the new square formed is smaller than the area of the rectangle by 27 cm²

  • xy = (y+3)²+27............ Equation 3

Substitute these values of x in equation 2 into equation 3

  • (y+9)(y) = (y+3)²+27
  • y²+9y = y²+6y+9+27
  • y²+9y = y²+6y+36

Collect like terms

  • y²-y²+9y-6y = 36
  • 3y = 36
  • y = 36/3
  • y = 12 cm.

Substitute the value of y into equation 1 to get x

  • x = 12+9
  • x = 21 cm.

  • Area of a rectangle = Length×width = 12×21 = 252 cm²

Hence, The area of the rectangle is 252 cm².

Learn more about rectangles here: https://brainly.com/question/24571594

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