The perimeter of a rectangle is 10 feet, and the area is 6 square feet. What is the width of the rectangle?

Question

The perimeter of a rectangle is 10 feet, and the area is 6 square feet. What is the width of
the rectangle?

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Orla Orla 5 years 2021-08-20T18:22:47+00:00 1 Answers 10 views 0

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  1. Jezebel
    0
    2021-08-20T18:24:06+00:00
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    Hello,

    Perimeter of a rectangle : 2 * (length + width)

    Area of a rectangle : length * width

    We know that the perimeter of the rectangle is equal to 10 feet and its area is equal to 6 square feet.

    Let’s call x the length of the rectangle and y the width of the rectangle. The pair (x ; y) verifies the following system :

    2 (x + y) = 10 ⇔ x + y = 5 ⇔ x = 5 – y

    x * y = 6 ⇔ (5 – y) * y = 6 ⇔ 5y – y² – 6 = 0 ⇔ y² – 5y + 6 = 0

    ⇔ y² – 3y – 2y + 6 = 0 ⇔ y(y – 3) – 2(y – 3) = 0 ⇔ (y – 2)(y – 3) = 0

    ⇔ y = 2 ou y = 3

    x = 5 – y ⇔ x = 5 – 2 or x = 3 – 2 ⇔ x = 3 or y = 2

    S = {(3 ; 2) ; (2 ; 3)}

    The width of the rectangle is 2 or 3 feet.

    🙂

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