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Marysya12 [62]
2 years ago
12

The length of the sides of a square measure 2x-5. The length of a rectangle measures 2x, and the width measures x + 2. For what

value of x is the perimeter of the square the same as the perimeter of the rectangle?
Mathematics
1 answer:
vladimir1956 [14]2 years ago
3 0

Answer:

x = 12

Step-by-step explanation:

Perimeter of a square:

The perimeter of a square of side x is given by:

P_s = 4x

Perimeter of a rectangle:

The perimeter of a rectangle of length l and width w is given by:

P_r = 2(l + w)

The length of the sides of a square measure 2x-5.

This means that the perimeter of the square is:

P_s = 4(2x - 5) = 8x - 20

The length of a rectangle measures 2x, and the width measures x + 2.

This means that the perimeter of the rectangle is:

P_r = 2(2x + x + 2) = 2(3x + 2) = 6x + 4

For what value of x is the perimeter of the square the same as the perimeter of the rectangle?

This is x for which:

P_s = P_r

So

8x - 20 = 6x + 4

8x - 6x = 20 + 4

2x = 24

x = \frac{24}{2}

x = 12

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