a perimeter of a trapezium is 55cm and its non parallel sides are 8 cm and 7cm the difference between the length of parallel sides is 5 cm. find the lengths of the parallel sides
draw ur trapezium & let d shorter parallel side =y &d longer=x
perimeter of trapezium=7+8+x+y=55
and x -y=5
==>x=5+y
substituting
15+5+y+y=55
20+2y=55
2y=55-20
=35
y=17.5
x=22.5
To find the lengths of the parallel sides of the trapezium, we can use a simple formula.
The formula for the perimeter of a trapezium is:
Perimeter = sum of all sides
In this case, we know that the perimeter is 55 cm, so we can write our equation as:
55 = side1 + side2 + side3 + side4
Now, let's assign variables to the unknown lengths. Let side1 and side2 be the lengths of the parallel sides, side3 be the shorter non-parallel side (7 cm), and side4 be the longer non-parallel side (8 cm).
Given that the difference between the length of the parallel sides is 5 cm, we can express this as:
side1 - side2 = 5
Now, we have a system of equations:
55 = side1 + side2 + 7 + 8
side1 - side2 = 5
To solve this system, we can use any method, such as substitution or elimination. Let's use the method of substitution.
From the second equation, we can express side1 in terms of side2:
side1 = side2 + 5
Now, we substitute this expression into the first equation:
55 = (side2 + 5) + side2 + 7 + 8
We simplify the equation:
55 = 2side2 + 20
Next, we isolate side2:
2side2 = 55 - 20
2side2 = 35
side2 = 35 / 2
side2 = 17.5 cm
Now, we can substitute this value of side2 back into the equation for side1:
side1 = 17.5 + 5
side1 = 22.5 cm
Therefore, the lengths of the parallel sides are 22.5 cm and 17.5 cm.