Question

The difference between two parallel sides of a trapezium is \[4\] cm. The perpendicular distance between them is $ 19 $ cm. If the area of the trapezium is $ 475\;c{m^2} $ then find the length of the parallel sides.

Answer 1

Hint: We will assume the length of the parallel sides first. In case of unknown terms assume any variable as the reference value. Then, use the formula for area of trapezium is equal to the half of the product of height with the sum of the length of its parallel sides and solve by substituting the known and unknown values to get the value of the assumed variable.

Complete step-by-step answer:
Let us suppose that the two parallel sides of the trapezium are “a” cm and “b” cm respectively.
Given that the difference between the two parallel sides of the trapezium is $ 4 $ cm.
 $ \Rightarrow a - b = 4{\text{ }}....{\text{ (1)}} $
Distance between the two lines, $ h = 19\;cm $
Area of the trapezium, $ A = 475\;c{m^2} $
We know that Area, $ A = \dfrac{1}{2}h(a + b) $
Place values in the above equation –
 $ \Rightarrow 475 = \dfrac{1}{2} \times 19 \times (a + b) $
When the term in the division changes its side, it goes to the multiplication, that is it goes to the numerator and vice-versa.
 $ \Rightarrow \dfrac{{475 \times 2}}{{19}} = (a + b) $
Simplify the above equation –
 $
   \Rightarrow 25 \times 2 = (a + b) \\
   \Rightarrow 50 = (a + b) \;
  $
Re-writing the above equation –
 $ \Rightarrow a + b = 50{\text{ }}....{\text{ (2)}} $
Add equations $ (1){\text{ and (2)}} $
 $ 2a = 54 $
When the term in the multiplication changes its sides, then it goes to the division
 $
   \Rightarrow a = \dfrac{{54}}{2} \\
   \Rightarrow a = 27\;cm \;
  $
Now place value of “a” in the equation $ (1) $
 $
   \Rightarrow a - b = 4 \\
   \Rightarrow 27 - b = 4 \;
  $
 When terms are moved from one side to another, the sign of the terms also changes. Positive changes to negative and negative changes to positive.
 $
   \Rightarrow 27 - 4 = b \\
   \Rightarrow b = 23\;cm \;
  $
Hence, the required answer- the lengths of the parallel sides are $ 27\;cm{\text{ and 23 cm}} $ respectively.
So, the correct answer is “ $ 27\;cm{\text{ and 23 cm}} $ ”.

Note: Do not forget to write the respective applicable units to the resultant answer. Remember the basic standard formulas to find the areas of the closed figures such as the quadrilaterals, square, rectangle, triangle and many more. The correct formula is most important in these types of sums. Rest do simplification carefully.