WILL GIVE BRAINLIEST!! If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a squa

Question

WILL GIVE BRAINLIEST!!
If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.

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Delwyn 4 years 2021-08-25T17:30:09+00:00 2 Answers 18 views 0

Answers ( )

  1. Sapo1
    0
    2021-08-25T17:31:13+00:00
    Reply

    Answer:

    The rectangle is 15 cm by 24 cm, and its area is 360 cm^2.

    hope this helps 🙂 plz brainliest

    Step-by-step explanation:

  2. thuthao
    0
    2021-08-25T17:31:57+00:00
    Reply

    Answer:

    \huge\boxed{\sf Area = 12.8 cm\²}

    Step-by-step explanation:

    Let,

    The length of rectangle = x

    The width of rectangle = y

    The length of square = x – 4

    The width of square = y + 5

    Area of rectangle = xy

    Area of square = xy + 40

    Condition No. 1:

    Area of Square = Length of square * Width of square

    xy + 40 = (x – 4)(y – 5)

    xy + 40 = xy – 5x – 4y + 20

    – 5x – 4y = 40 – 20

    – 5x – 4y = 20

    5x + 4y = -20 ——————(1)

    Condition No. 2:

    We know that:

    Length of square = Width of square

    x – 4 = y + 5

    Add 4 to both sides

    x = y + 5 + 4

    x = y + 9 —————————(2)

    Solution:

    Put Eq. (2) in (1)

    5 (y + 9) + 4y = -20

    5y + 45 + 4y = -20

    9y + 45 = -20

    9y = -20-45

    y = -65 / 9

    Now, Put the value of y in Eq. (2)

    x = (-65 / 9) + 9

    x = (-65 + 81) / 9

    x = 16 / 9 cm

    Now,

    Area of rectangle = xy

    Area = ( -65 / 9 ) * ( 16 / 9 )

    Area = (-65*16) / (9*9)

    Area = -1040/81

    Area = 12.8 cm² (Neglecting -ve sign)

    \rule[225]{225}{2}

    Hope this helped!

    ~AH1807

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