Question
The difference between two parallel sides of a trapezium is 8cm. The perpendicular distance between them is 19cm while the area of trapezium is 760 sq.cm. What will be the lengths of the parallel sides.
Hint:
Given , the difference between parallel sides ; we find the sum of lengths of
the parallel side from the area of trapezium formula by substituting the given values.
Now ,equate both the equations to get the values of lengths of parallel sides.
The correct answer is: 30.5 and 49.5
Ans :- 30.5 cm ; 49.5 cm
Explanation :-
Let the length of parallel side be x and y where (x<y)
Step 1:- frame the equation based on given conditions
Difference between parallel side = y-x = 8 —- Eq1
Given area of trapezium = 760 sq.cm
Perpendicular distance or height = 19 cm .
![text Area of trapezium end text equals 1 half left parenthesis text height end text right parenthesis left parenthesis text sum of lengths of parallel sides end text right parenthesis](data:image/png;base64,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)
![not stretchy rightwards double arrow 760 equals 1 half left parenthesis 19 right parenthesis text (sum of lengths of parallel sides) end text](data:image/png;base64,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)
—- Eq2
Step 2:- eliminate x to find y
Adding Eq1 + Eq2 to eliminate x
![y minus x plus x plus y equals 19 plus 80 not stretchy rightwards double arrow 2 y equals 99 not stretchy rightwards double arrow y equals 49.5 cm](data:image/png;base64,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)
Step 3:- Find x by substituting the value of y in Eq 2 .
![x plus y equals 80 cm not stretchy rightwards double arrow x plus 49.5 equals 80 not stretchy rightwards double arrow x equals 30.5 cm](data:image/png;base64,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)
Therefore, 30.5 cm and 49.5 cm are the lengths of the parallel sides of trapezium.
Related Questions to study
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
The sum of 3 consecutive natural numbers is 75. Find the numbers.
The sum of 3 consecutive natural numbers is 75. Find the numbers.
Find three consecutive even numbers whose sum is 312.
Find three consecutive even numbers whose sum is 312.
![](data:image/png;base64,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)
Triangles ABC and DEF above are similar. How much longer than segment EF is segment DE ?
Note:
There are three ways to prove that two triangles are similar- AAA,
SAS, SSS.
AAA means that the corresponding angles are equal,
SAS means two sides of the triangles are in equal ratio and the angles between these two sides are equal,
SSS means that all three corresponding sides have equal ratio
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)
Triangles ABC and DEF above are similar. How much longer than segment EF is segment DE ?
Note:
There are three ways to prove that two triangles are similar- AAA,
SAS, SSS.
AAA means that the corresponding angles are equal,
SAS means two sides of the triangles are in equal ratio and the angles between these two sides are equal,
SSS means that all three corresponding sides have equal ratio
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm, and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, Find the volume of the wood and that of the graphite?
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm, and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, Find the volume of the wood and that of the graphite?
The load capacity of a certain washing machine is 12 pounds. What is the approximate load capacity of the same washing machine, in kilograms?
( 1 kilogram = 2.2046 pounds)
Note:
There are many other units of weight such as ton, ounce, gram, stone, grain, milligram, etc. There is conversion formula for each of these pairs, for eg.
1 kilogram = 35.27 ounce= 0.16 stone= 1000 gram
1 pound= 16 ounce= 0.07 stone= 435.60 gram
The load capacity of a certain washing machine is 12 pounds. What is the approximate load capacity of the same washing machine, in kilograms?
( 1 kilogram = 2.2046 pounds)
Note:
There are many other units of weight such as ton, ounce, gram, stone, grain, milligram, etc. There is conversion formula for each of these pairs, for eg.
1 kilogram = 35.27 ounce= 0.16 stone= 1000 gram
1 pound= 16 ounce= 0.07 stone= 435.60 gram