Question

The Dig It Project is designing two gardens that have the same perimeter. One garden is a trapezoid whose nonparallel sides are equal. The other is a quadrilateral. Two possible designs are shown on the right.

Suppose the Dig It Project wants the perimeter of each garden to be 60 meters. What is the value of x in this case? How did you find this?

Answer 1

Step-by-step explanation:

hi

Answer 2

To find the value of x for the gardens with the same perimeter, set up an equation based on the given information. The value of x for the second design is 15 meters.

Step-by-step explanation:

To find the value of x for the gardens with the same perimeter, we need to set up an equation based on the given information. Let's consider the design of the first garden, which is a trapezoid with nonparallel sides that are equal in length. The perimeter of a trapezoid can be calculated by adding up the lengths of all its sides. In this case, the perimeter is given as 60 meters. Let the lengths of the nonparallel sides of the trapezoid be x. The lengths of the parallel sides can be determined using this information. The longer parallel side can be calculated as 60 - 2x, and the shorter parallel side is x.

So, the perimeter of the trapezoid = x + x + (60 - 2x) + (60 - 2x) = 60

4x + 120 - 4x = 60

120 = 60

Since this equation is not true, it means that the design of the first garden does not satisfy the given condition of having the same perimeter. We can conclude that the first design is not valid.

Now let's consider the design of the second garden, which is a quadrilateral. Since a quadrilateral has four sides, each side is equal to one-fourth of the perimeter. So, each side will be 60 / 4 = 15 meters. Therefore, the value of x for the second design is 15 meters.