a trapezium with its parallel sides in the ratio16:5,is cut from a rectangle whose sides measure 63m &5m respectively. the area of the trapezium is 4/15 of the rectangle .find the lengths of the parallel sides of the trapezium.
area of rectangle is 63x5 or 315 cm^2
Let the two parallel sides by 16x and 5x.
area of trap = (average of 2 parallel sides)(height)
= ((16x + 5x)/2)(5) = (4/15)(315)
105x/2 = 84
105x = 168
x = 8/5 = 1.6
The two sides are 25.6 and 8
check:
area = (25.6+8)/2(5) = 84
and (4/15)(315) = 84
To find the lengths of the parallel sides of the trapezium, we can use the given information about the ratio of the parallel sides and the area of the trapezium.
Let's assume the length of the parallel sides of the trapezium are 16x and 5x, where x is a common multiplier. The height of the trapezium can also be determined using the given information.
Area of the trapezium = (1/2) × Sum of parallel sides × Height
Given that the area of the trapezium is (4/15) of the rectangle, and the dimensions of the rectangle are 63m and 5m respectively, we can calculate the area of the rectangle:
Area of the rectangle = Length × Width = 63m × 5m = 315m²
Now, the area of the trapezium is (4/15) of the rectangle's area:
Area of the trapezium = (4/15) × Area of the rectangle = (4/15) × 315m² = 84m²
Using the area formula, we can write:
84m² = (1/2) × (16x + 5x) × Height
Simplifying the equation:
84m² = (21x) × Height
Now, we need to find the height of the trapezium. To do that, we need another piece of information.
Do you have any additional information about the height of the trapezium, or any other information that might help us solve the problem?