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    a preschool has a rectangular field and a rectangular playground that are similar in shape. each dimension of the field is 3.2 times the corresponding dimension of the playground. which statement is true?

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    A preschool has a rectangular field and rectangular playground that are similar in shape. Each dimension of the field is 3.2 times the corresponding dimensions of the playground. Which statement is true? A. The area of the field is 6.4 times the area of

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    Question:

    A preschool has a rectangular field and rectangular playground that are similar in shape. Each dimension of the field is 3.2 times the corresponding dimensions of the playground. Which statement is true?

    A. The area of the field is 6.4 times the area of the playground.

    B. The area of the field is 10.24 times the area of the playground.

    C. The perimeter of the field is 6.4 times the perimeter of the playground.

    D. The perimeter of the field is 10.24 times the perimeter of the playground.

    Area and Perimeter of Rectangle:

    A rectangle is a closed polygon made up of four sides. The opposite sides of the rectangle are parallel and equal to each other. The adjacent sides of the rectangle make right angles with each other. The area of a rectangle is the product of its adjacent sides. The longer side is known as the length

    l l

    and the shorter side is known as the width

    w w . A = l ⋅ w A=l⋅w

    The perimeter of a rectangle is twice the sum of its adjacent sides.

    P = 2 ( l + w ) P=2(l+w)

    Answer and Explanation:

    Let the length and width of the rectangular playground be

    l l and w w

    , respectively. Find the area of the playground

    A p Ap . A p = l ⋅ w = l w Ap=l⋅w=lw

    Find the perimeter of the playground

    P p Pp . P p = 2 ( l + w ) Pp=2(l+w)

    The length of the field is

    3.2 l 3.2l

    and the width of the field is

    3.2 w 3.2w

    . Find the area of the field

    A f Af . A f = 3.2 l ⋅ 3.2 w = 10.24 l w

    Af=3.2l⋅3.2w=10.24lw

    The area of the field is

    10.24 l w 10.24lw

    , which is equivalent to

    10.24 10.24

    times the area of the playground.

    Hence, and therefore, statement A is incorrect.

    Find the perimeter of the field

    P f Pf . P f = 2 ( 3.2 l + 3.2 w ) = 2 ⋅ 3.2 ( l + w ) = 6.4 ( l + w )

    Pf=2(3.2l+3.2w)=2⋅3.2(l+w)=6.4(l+w)

    Hence, the perimeter of the field is

    6.4 ( l + w ) 6.4(l+w)

    , which is equivalent to

    3.2 3.2

    times the perimeter of the playground. Hence, statements C and D are incorrect.

    Thus, the correct answer is B. The area of the field is 10.24 times the area of the playground.

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    The area of the field is 10.24 times the area of the playground.

    The perimeter of the field is 6.4 times the perimeter of the playground.

    The perimeter of the field is 10.24 times the perimeter of the playground.

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    17. A preschool has a rectangular field and a rectangular playground that are similar in shape.

    17. A preschool has a rectangular field and a rectangular playground that are similar in shape. Each - 15907762

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    17. A preschool has a rectangular field and a rectangular playground that are similar in shape. Each

    dimension of the field is 3.2 times the corresponding dimension of the playground. Which statement

    is true?

    A. The area of the field is 6.4 times the area of the playground.

    B. The area of the field is 10.24 times the area of the playground.

    C. The perimeter of the field is 6.4 times the perimeter of the playground.

    D. The perimeter of the field is 10.24 times the perimeter of the playground.​

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