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
let the longer of the parallel sides be x
then the shorter of the parallel sides is x-5
solve for x :
x + x-5 + 8 + 7 = 55
then sub back in for x and x-5
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x+x-5+7+8=55
2x-5+15=55
2x+10(15-5)=55
2x= 55-10 (= right side sign changes to -)
2x= 45
x=45/2
x= 22.5
1 parallel side = 22.5 cm
since another parallel side= -5 hence
22.5-5= 17.5
To find the lengths of the parallel sides of the trapezium, we can use the given information about the perimeter and the non-parallel sides.
Let's denote the lengths of the parallel sides as a and b.
Given:
Perimeter of the trapezium = 55 cm
Non-parallel sides = 8 cm and 7 cm
Difference between the lengths of parallel sides = 5 cm
The formula for the perimeter of a trapezium is P = a + b + c + d, where a and b are the lengths of the parallel sides, and c and d are the lengths of the non-parallel sides.
In this case, c = 8 cm and d = 7 cm.
We know that a - b = 5 cm (difference between the lengths of the parallel sides).
Now, let's substitute the values into the trapezium perimeter formula:
55 cm = a + b + 8 cm + 7 cm
Simplifying the equation, we have:
55 cm = a + b + 15 cm
We also have the equation: a - b = 5 cm
To solve these equations simultaneously, we can use the method of substitution or elimination.
Let's rearrange the second equation to express 'a' in terms of 'b':
a = b + 5 cm
Now, substitute the value of 'a' in the first equation:
55 cm = (b + 5 cm) + b + 15 cm
Simplifying the equation:
55 cm = 2b + 20 cm
Subtract 20 cm from both sides:
55 cm - 20 cm = 2b
Simplifying further:
35 cm = 2b
Divide by 2:
b = 17.5 cm
Now, substitute the value of 'b' back into the equation for 'a':
a = 17.5 cm + 5 cm
a = 22.5 cm
Therefore, the lengths of the parallel sides are:
Side a = 22.5 cm
Side b = 17.5 cm