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4 December, 00:13

The length of a rectangle is (x + 5) inches long, and the width is 3 2/5 inches. If the area is 51 square inches. Write and solve and equation to find the length of the rectangle

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  1. 4 December, 00:36
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    Length = 15 inches

    Step-by-step explanation:

    Let L represent the Length, W, the width and A, the area of the rectangle

    from the question;

    L = x + 5 ... eq 1

    W = 3 2/5

    Changing the value of W into an improper fraction; W = 17/5

    A = 51 inches

    Area of a rectangle, A = Lenght x Width

    A = L X W ... eq 2

    slotting the values of A, L and W in eq 2

    51 = (x + 5) X 17/5

    51 = (17/5x) + (17/5 X 5)

    51 = 17/5x + 17

    51 = 17x + 85

    5

    Cross multiply

    5 X 51 = (17x + 85) X 1

    255 = 17x + 85

    Subtracting 85 from both sides

    255 - 85 = 17x + 85 - 85

    170 = 17x

    Dividing both sides by the coefficient of x which is 17

    10 = x

    Therefore, x = 10

    Slotting in the value of x in eq 2

    L = 10 + 5

    L = 15 inches

    Let's check our answer by slotting in the values of A, W and L in eq 1

    51 = 15 X 17/5

    51 = 3 X 17

    51 = 51

    Since both sides of the equation are equal, the value of L is correct
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