Question

The perimeter of the rectangle and the triangle shown are the same. Write an equation to represent the situation, and solve for x. Then, find the perimeter of each shape.

2x+10=3x+6, x=4, Rectangle Perimeter = 18, Triangle Perimeter = 16
b) 3x+10=2x+6, x=−4, No solution
c) 2x+10=x+6, x=−4, No solution
d) 3x+10=2x+4, x=−6, Rectangle Perimeter = 22, Triangle Perimeter = 16

Answer 1

To solve the equation 2x+10=3x+6 for x, subtract 2x from both sides and simplify. The perimeter of the rectangle is 44 units. The perimeter of the triangle cannot be determined from the given equation.

Step-by-step explanation:

To solve the equation 2x+10=3x+6 for x, we need to isolate x on one side of the equation. First, subtract 2x from both sides to get 10 = x+6. Then, subtract 6 from both sides to get 4 = x. So, x = 4.

To find the perimeter of the rectangle, substitute x = 4 into the length and width of the rectangle. If the length is 2x+10, then the length would be 2(4)+10 = 8+10 = 18. Similarly, the width would be 4. So, the perimeter of the rectangle is 2(18+4)=<<2*(18+4)=44>>44.

Next, to find the perimeter of the triangle, we need to know the length of all three sides. However, the problem does not provide enough information about the triangle. So, we cannot determine the perimeter of the triangle from the given equation.