A trapezium has area 1760 and the distance between its parallel sides is 40. If one parallel side is 39, what is the other side?
To answer this question, we need to recall the formula for calculating the area of a trapezium. If the length of the parallel sides of the trapezium are 𝑙 one and 𝑙 two and the perpendicular distance between them is ℎ, then the area of the trapezium is given by one-half multiplied by ℎ multiplied by the sum of 𝑙 one and 𝑙 two.
In this question, we’re told three other pieces of information in this formula. We know one of the parallel sides is 39, the distance between the parallel sides ℎ is 40, and the area is 1760. So we can substitute these values into the formula. We have one-half multiplied by 40 multiplied by 39 plus 𝑙 two is equal to 1760.
In order to find the value of 𝑙 two, the length of the other parallel side, we need to solve this equation. We can simplify the left-hand side of the equation slightly by replacing one-half multiplied by 40 with 20.
Now, let’s solve this equation. The first step is to divide both sides by 20. This gives 39 plus 𝑙 two is equal to 88. The final step in solving this equation is to subtract 39 from each side. This gives 𝑙 two is equal to 49. So the length of the second parallel side of this trapezium is 49 units.