The perimeter of an isosceles trapezium ( having non-parallel sides equal ) is 7.07 cm. If the parallel sides of the trapezium measure 37/20 cm and 58/25 cm, find the measure of the equal non parallel sides.
let each of the non-parallel sides be x cm
x + x + 37/20 + 58/25 = 7.07
solve for x, I suggest changing the two fractions to decimals, they come out exact.
To find the measure of the equal non-parallel sides of the trapezium, we can use the formula for the perimeter of a trapezium.
The perimeter of a trapezium is given by the sum of all its sides. In this case, we have two parallel sides and two non-parallel sides.
Let's call the measure of the equal non-parallel sides as "x" cm.
The formula for the perimeter of a trapezium is:
Perimeter = Sum of all sides = Sum of parallel sides + Sum of non-parallel sides
The given parallel sides measure 37/20 cm and 58/25 cm.
So, the sum of the parallel sides is:
(37/20) cm + (58/25) cm = [(37 * 25) + (58 * 20)] / (20 * 25) = (925 + 1160) / 500 = 2085 / 500 = 4.17 cm
The perimeter of the trapezium is given as 7.07 cm.
Therefore, the sum of the non-parallel sides is:
Perimeter of trapezium - Sum of parallel sides = 7.07 cm - 4.17 cm = 2.9 cm
Since the trapezium has two equal non-parallel sides, we can divide the sum of the non-parallel sides by 2 to get the measure of each side:
Each non-parallel side = 2.9 cm / 2 = 1.45 cm
Hence, the measure of the equal non-parallel sides of the trapezium is 1.45 cm.