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What is #x# if the perimeter of a rectangle with sides of #x# and #2x + 6# is #27# in?

Answer 1

Violet Aldrich

#x=5/2#

The perimeter of a rectangle is the sum of all its sides.

Each rectangle has #2# pairs congruent sides.

Thus, the sides of the rectangle are:

#x# #x# #2x+6# #2x+6#

Since these are the sides, their sum will be equal to the perimeter, #27#.

#x+x+2x+6+2x+6=27#

#6x+12=27#

#6x=15#

#x=15/6#

#x=5/2#

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Answer 2

Sophia Alfred

To find the value of ( x ) in this problem, we use the formula for the perimeter of a rectangle, which is ( P = 2l + 2w ), where ( l ) is the length and ( w ) is the width. In this case, we are given that the length is ( x ) and the width is ( 2x + 6 ), and the perimeter is 27 inches.

So, we have:

[ 27 = 2x + 2(2x + 6) ]

[ 27 = 2x + 4x + 12 ]

[ 27 = 6x + 12 ]

Subtracting 12 from both sides:

[ 15 = 6x ]

Dividing both sides by 6:

[ x = \frac{15}{6} ]

[ x = \frac{5}{2} ]

Therefore, the value of ( x ) is ( \frac{5}{2} ) inches.

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Answer from HIX Tutor

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