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.