Question

The sum of the lengths of the bases of a trapezium whose altitude is 24 m and whose area is 144 m² is:

a) 3 m

b) 6 m

c) 9 m

d) 12 m

Answer 1

The sum of the lengths of the bases of a trapezium with a 24 m altitude and an area of 144 m² is 12 m, corresponding to option (d).

Step-by-step explanation:

The sum of the lengths of the bases of a trapezium with an altitude of 24 m and an area of 144 m² can be found using the formula for the area of a trapezium, which is given by the average of the bases multiplied by the altitude. In formulaic terms, Area = ½ * (base1 + base2) * altitude.

To find the sum of the lengths of the bases (base1 + base2), we rearrange the formula to solve for this sum:

• Sum of bases = (2 * Area) / altitude

Upon substituting the given values, we get:

• Sum of bases = (2 * 144 m²) / 24 m = 288 m² / 24 m = 12 m

Therefore, the sum of the lengths of the bases of the trapezium is 12 meters, which corresponds to option (d).