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Alex73 [517]
3 years ago
12

- (8x + 6) =90" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Lina20 [59]3 years ago
8 0

Answer:

x=12

Step-by-step explanation:

16x - (8x  + 6) =90

The first step is to distribute the - sign

16x -8x -6 =90

Now we combine the like terms

8x-6 = 90

Add 6 to each side

8x-6+6 = 90+6

8x = 96

Divide each side by 8

8x/8 = 96/8

x =12

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<em>The length of the square​ that has the same perimeter as the rectangle is of length 6cm and area of 48cm² is 7cm</em>

<h2>Explanation:</h2>

Let's call:

A_{s}:Area \ of \ square \\ \\ A_{r}:Area \ of \ rectangle \\ \\ P_{s}:Perimeter \ of \ square \\ \\ P_{r}:Perimeter \ of \ rectangle

From the question, we know that:

  • <em>A rectangle and a square have the same perimeter.</em>

So:

P_{s}=P_{r}

Moreover:

  • <em>The rectangle is of length 6cm and has an area of 48cm²</em>

Accordingly:

For \ Rectangle: \\ \\ L:Length \\ W:Width \\ \\ A_{r}=L\times W \\ \\ 48=6W \\ \\ W=8

Also:

A_{s}=s^2 \\ \\ S:Side \ of \ square

From the statement of perimeters:

P_{s}=P_{r} \\ \\ \\ But: \\ \\ P_{s}=4s \\ \\ P_{r}=2W+2L \\ \\ \\ Then: \\ \\ 4s=2W+2L \\ \\ \\ But: \ W=8 \ and \ L=6 \\ \\ 4s=2(8)+2(6) \\ \\ 4s=16+12 \\ \\ 4s=28 \\ \\ \boxed{s=7cm}

Finally, <em>the length of the square​ that has the same perimeter as the rectangle is of length 6cm and area of 48cm² is 7cm</em>

<h2>Learn more:</h2>

Perimeter: brainly.com/question/9969486

#LearnWithBrainly

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