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Which expression is correct u must have an explanation

Which expression is correct u must have an explanation-example-1
User Splrs
by
7.9k points

1 Answer

7 votes

Answer:

B

Explanation:

the perimeter (one time all around the object) of a rectangle is of course

2×length + 2×width

now, as the length = 4×width, we get a perimeter

2×(4×width) + 2×width

2×a = a + a

that is the principle of multiplication (remember elementary school ?)

so, the right answers are

2(4w) + 2(w)

or

4w + 4w + w + w

which is because of the commutative property of addition and correspondingly multiplication

w + w + 4w + 4w

and now, let's add up all these "w" :

1w + 1w + 4w + 4w = 10w

therefore

A, C and D are correct.

in other words, only B is wrong.

because 2(w . 4w) = 2×4w² = 8w²

8w² = 10w

is not true for all values of w.

e.g. w = 2

8×2² = 10×2

32 = 20

is not true.

therefore 8w² is not the same as the correctly calculated 10w, and it is therefore not a correct expression for the perimeter.

User Laerion
by
7.6k points

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