Question

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Answer 1

Hello!

Answer:

`\Large \boxed{\sf x =7}`

Explanation:

We want to find the value of x.

We know that the two figures have the same perimeter.

Let's calculate the perimeter of each figure:

Rectangle:

`\sf P = 2(l+w) = 2(x+5+8) = 2(x+13) = 2x+26`

Square:

`\sf P = 4(x+3) = 4x+12`

So, now, we have this equation:

`\sf 2x+26=4x+12`

Let's solve this equation to find the value of x:

▪ First, subtract 2x from both sides:

`\sf 2x+26-2x=4x+12-2x`

Simplify:

`\sf 26=2x+12`

▪ Next, subtract 12 from both sides:

`\sf 26-12=2x+12-12`

Simplify:

`\sf 2x=14`

▪ Finally, divide both sides by 2:

`\sf (2x)/(2) = (14)/(2)`

Simplify:

`\boxed{\sf x =7}`

Check:

Let's calculate the perimeters of each figure with x = 7:

Rectangle:

`\sf P = 2(7+5+8) = 2(20) = 40cm`

Square:

`\sf P=4(7+3) = 4(10) = 40cm`

✔ So the check is good.

Conclusion:

The value of x is 7 cm.