The area of a trapezium is 475 cm2 and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other
Question
The area of a trapezium is 475 cm2 and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other
Solution
Let's denote the shorter parallel side of the trapezium as 'a' (in cm). According to the problem, the longer parallel side is 'a + 4' cm.
The formula for the area (A) of a trapezium is given by:
A = 1/2 * (sum of the lengths of the parallel sides) * height
We can substitute the given values into this formula:
475 cm² = 1/2 * (a + a + 4) * 19 cm
Solving this equation will give us the lengths of the two parallel sides.
First, simplify the equation:
475 = 1/2 * (2a + 4) * 19
475 = (a + 2) * 19
Divide both sides by 19:
a + 2 = 475 / 19
a + 2 = 25
Subtract 2 from both sides to solve for 'a':
a = 25 - 2
a = 23 cm
So, the shorter parallel side (a) is 23 cm, and the longer parallel side (a + 4) is 23 + 4 = 27 cm.
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