Rectangle Perimeter Equation: Solving for X when X+2 and X are Adjacent Sides (30cm)

A rectangle has a perimeter measuring 30 cm.

One side of the rectangle is 2 cm longer than the adjacent side.

Calculate the length of the rectangle's shorter sides.

X+2X+2X+2XXX

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Step-by-step video solution

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00:00 Calculate the shorter side of the rectangle
00:03 The side according to the given data
00:08 In a rectangle, opposite sides are equal
00:19 The length of the side according to the given data
00:22 In a rectangle, opposite sides are equal
00:29 The perimeter of the rectangle equals the sum of its sides
00:39 Insert the appropriate values into the formula according to the given data and solve for X
00:55 Collect like terms
01:04 Isolate X (the small side)
01:14 This is the solution

Step-by-step written solution

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1

Understand the problem

A rectangle has a perimeter measuring 30 cm.

One side of the rectangle is 2 cm longer than the adjacent side.

Calculate the length of the rectangle's shorter sides.

X+2X+2X+2XXX

2

Step-by-step solution

Since every pair of opposite sides in a rectangle are equal, we know that:

AB=CD=x+2 AB=CD=x+2

AD=BC=x AD=BC=x

We can then create the following equation based on the given data:

30=x+x+2+x+x+2 30=x+x+2+x+x+2

30=4x+4 30=4x+4

30−4=4x 30-4=4x

26=4x 26=4x

x=6.5 x=6.5

3

Final Answer

6.5 6.5

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\( 100+5-100+5 \)

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