# An equation about a rectangle with given perimeter

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## Solution 1

For the perimeter of a rectangle, we know that the perimeter is the sum of the lengths of all its sides. In a rectangle, opposite sides are equal in length.

$$\text{Perimeter}\; = 2\times\;\text{length}\; + 2\times\;\text{width}$$

$$2(x - 2)+ 2(2x +1) = \color{blue}{2x} \color{red}{\bf -4} + \color{blue}{4x} + \color{red}{\bf 2} =43$$ $$\color{blue}{6x} \color{red}{\bf - 2} = 43$$ $$6x -2 + {\bf 2} = 43 + {\bf 2}$$ $$6x = 45$$ $${\ Khc 16} \times 6x = {\bf \dfrac 16} \times 45$$ $$x = \dfrac {45}{6} = \dfrac{{\bf 3}\times 15}{{\bf 3} \times 2} =\dfrac {15}{2}$$

$$\text{This gives us}\;\;x = \frac{15}{2} = 7\frac12 = 7.5\;\text{cm}$$

## Solution 2

The perimeter is the sum of the 4 sides of the rectangle. Hence $$43=2(x-2)+2(2x+1) \iff 43=2x-4+4x+2 \iff 43=6x-2 \iff 6x=45 \iff x=\frac{45}{6}$$

## Solution 3

The perimeter $P$ of the rectangle has length 43, and we also know that the sum of the lengths of each edge is $(x-2)+(x-2)+(2x+1)+(2x+1)$. So, from this we get $P=43$ and $P=(x-2)+(x-2)+(2x+1)+(2x+1)$. So, $$(x-2)+(x-2)+(2x+1)+(2x+1)=43.$$ Can you simplify and solve this equation?

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### crmepham

I am currently coding in Java, Kotlin and Go.

Updated on February 14, 2020

• crmepham over 2 years

I am doing a revision calculator paper and am stuck on an algebra question.

There is a picture of a rectangle. One side is $x-2,$ another side is $2x +1.$

The question is. Setup and solve an equation to work out the value of $x.$

The perimeter of this rectangle is $43$cm.

How do I do this? Sorry I am useless with algebra, and its worth 5 marks. Thanks

• Dan Rust about 9 years
Are you given any other information? Maybe the area of the rectangle, perimeter length of the rectangle or length of the diagonal of the rectangle?
Not quite. From the center equation, we can simplify the left hand side to get $6x-2=43$ and so if we rearrange this (by first adding $2$ to both sides, and then diving by 6) we get $x=\frac{45}{6}=7.5$.