Question

a square and equilateral triangle have the same perimeters. the length of a side of the triangle is 4x+2 inches. The length of a side if the square is 2x+2 inches. Write and solve an equation to find the side length of the triangle, the side length of the square and their perimeter

Answer 1

To find the side lengths and perimeters of the triangle and square, set up equations using the given information and solve for x. Substitute the value of x back into the equations to find the side lengths. Multiply the side length by the number of sides to find the perimeters.

Step-by-step explanation:

To find the side length of the equilateral triangle, you can set up an equation using the given information. The equation would be: 4x+2 = 2x+2. Simplifying, you get: 2x = 0, which means x = 0.

Substituting this value back into the equation, you can find the side length of the triangle: 4(0)+2 = 2 inches.

Similarly, for the square, the equation would be: 2x+2 = 8. Simplifying, you get: 2x = 6, which means x = 3.

Substituting this value back into the equation, you can find the side length of the square: 2(3)+2 = 8 inches.

Finally, to find the perimeters of both shapes, you can multiply the side length by the number of sides. The perimeter of the triangle is: 3 * 2 = 6 inches. The perimeter of the square is: 4 * 8 = 32 inches.