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.
If each of the sloping sides is h, then we have
2h+1.85+2.32=7.07
h = 1.45 = 29/20
To find the measure of the equal non-parallel sides, we can use the formula for the perimeter of an isosceles trapezium.
The formula for the perimeter of an isosceles trapezium is given by:
Perimeter = sum of lengths of all sides
In this case, we have two parallel sides and two equal non-parallel sides.
Let's denote the lengths of the parallel sides as a and b, and the lengths of the non-parallel sides as x.
Given:
Length of the first parallel side (a) = 37/20 cm
Length of the second parallel side (b) = 58/25 cm
Perimeter of the trapezium = 7.07 cm
Using the formula for the perimeter, we can write:
7.07 = a + b + 2x
Substituting the given values, we have:
7.07 = 37/20 + 58/25 + 2x
To solve this equation for x, we can rearrange it as follows:
7.07 = (37/20) + (58/25) + 2x
Multiply all the terms by 100 to clear the fractions:
7.07 * 100 = (37/20) * 100 + (58/25) * 100 + 2x * 100
707 = 1850/20 + 2320/25 + 200x
Simplify the fractions:
707 = 92.5 + 92.8 + 200x
Combine like terms:
707 = 185.3 + 200x
Rearrange the equation:
707 - 185.3 = 200x
521.7 = 200x
Divide both sides by 200:
521.7/200 = x
x ≈ 2.61
Therefore, the measure of the equal non-parallel sides (x) is approximately 2.61 cm.