This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5
This is an important ques
The lengths of the parallel sides of a trapezium are (x + 9) cm and (2x – 3) cm and the distance between them is (x + 4) cm. If its area is 540 cm², find x.
Question no.17 , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,
Solution:
We know that,
Area of a trapezium = ½ × (sum of parallel sides) × (height)
Given, the length of parallel sides are (x + 9) and (2x – 3)
And height = (x + 4)
Now, according the conditions in the problem
½ × (x + 9 + 2x – 3) × (x + 4) = 540
(3x + 6) (x + 4) = 540 × 2
3x2 + 12x + 6x + 24 = 1080
3x2 + 18x – 1056 = 0
x2 + 6x – 352 = 0 [Dividing by 3]
By factorization method, we have
x2 + 22x – 16x – 352 = 0
x(x + 22) – 16(x + 22) = 0
(x – 16) (x + 22) = 0
So,
x – 16 = 0 or x + 22 = 0
x = 16 or x = -22
As measurements cannot be negative x = -22 is not possible
Therefore, x = 16