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The perimeter of Figure 1 is four times a number minus three.
The perimeter of Figure 2 is two times the same number plus five. The perimeters
of Figure 1 and Figure 2 are the same.
a. Write an equation to find the number.
b. Solve the equation to find the number.
c. What is the perimeter of Figure 2? Explain.
d. Find the perimeter of Figure 1. Compare the perimeter of Figure
perimeter you found for Figure 2 to justify the value of k is correct.



Answer :

The answers to all the subparts are:

  • (A) The number will be found using the equation 4x-3 = 2x +5.
  • (B) We obtain a value of 4 after solving the equation.
  • (C) Figure 2's perimeter will be equal to 13.

What is the circumference?

  • The perimeter of a shape is the distance around its edge.

So, there have been two figures provided.

  • Figure 1's perimeter is four times a number minus three, whereas Figure 2's perimeter is two times the same number plus five.
  • Based on the data provided, we must solve the given subparts of the question.

Let x be the number.

  • Figure 1's perimeter will be equal to 4x - 3.
  • Figure 2's perimeter will be equal to 2x + 5.

(A) According to the question, the perimeters of both figures are equal.

As a result, the equation will be:

  • 4x-3 = 2x+5

(B) By solving the equation:

  • 4x -3 = 2x + 5
  • 4x-2x = 3 + 5
  • 2x = 8
  • x = 4

As a result, the answer is 4.

(C) Figure 2 perimeter = 2x + 5

  • = (2 × 4) + 5
  • = 13

As a result, the perimeter of figure 2 equals 13.

Therefore, the answers to all the subparts are:

  • (A) The number will be found using the equation 4x-3 = 2x +5.
  • (B) We obtain a value of 4 after solving the equation.
  • (C) Figure 2's perimeter will be equal to 13.

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