Question

There is a quadrilateral with a perimeter of 20 cm. Three sided length are 1/5 of the perimeter, 3/10 of the perimeter, and 3/15 of the perimeter. How long is the fourth side length? What is the name of this quadrilateral? Show steps.

Answer 1

Let the lengths of the three sides be x, y, and z, where:

x = 1/5(20) = 4 cm
y = 3/10(20) = 6 cm
z = 3/15(20) = 4 cm

Now, we know that the perimeter of a quadrilateral is equal to the sum of all four sides. Therefore, the sum of the three known sides x, y, and z is 4 + 6 + 4 = 14 cm.

Let the length of the fourth side be w cm. We know that the perimeter of the quadrilateral is 20 cm. Therefore, we can write the equation:

x + y + z + w = 20

Substitute the values of x, y, z, and the sum of the three known sides into the equation:

4 + 6 + 4 + w = 20
14 + w = 20
w = 20 - 14
w = 6

Therefore, the length of the fourth side is 6 cm.

This quadrilateral is called a trapezoid - a quadrilateral with at least one pair of parallel sides.