The area of a trapezium is 200 cm\(^2\). Its parallel sides are in the ratio 2 : 3 and the perpendicular distance between them is 16 cm. Find the length of each of the parallel sides
10 cm and 15 cm
8 cm and 12 cm
6 cm and 9 cm
12 cm and 18 cm
Correct answer is A
Area of trapezium = \(\frac{1}{2}(a + b) h\)
⇒ \(\frac{1}{2} (a + b)\times 16 = 200\)
⇒ 8(a + b) = 200
⇒ a + b = \(\frac{200}{8}\) = 25 -----(i)
⇒ a : b = 2 : 3
⇒ \(\frac{a}{b} = \frac{2}{3}\)
⇒ 3a = 2b
⇒ a = \(\frac{2b}{3}\) -------(ii)
Substitute \(\frac{2b}{3}\) for a in equation (i)
⇒ \(\frac{2b}{3}\) + b = 25
\(\frac{5b}{3}\) = 25
⇒ b = 25 ÷ \(\frac{5}{3} = 25\times\frac{3}{5} = 15cm\)
From equation (ii)
⇒ a = \(\frac{2 \times 15}{3} = 2\times5 = 10cm\)
∴ Lengths of each parallel sides are 10cm and 15cm
Similar Questions
Differentiate \((2x+5)^{2} (x-4)\) with respect to x. ...
Solve the equation x2 - 3x - 10 = 0...
Simplify(0.3 x 105) \(\div\) (0.4 \(\times\) 107), leaving you answer in the standard form....
Find the probability that a number selected at random from 41 to 56 is a multiply of 9...
Calculate the value of x and y if (27x รท 81x+2y = 9 ,x + 4y = 0...
Simplify 213\(_4\) x 23\(_4\) ...
What is the Value of 11101\(_{two}\)+ 10011\(_{two}\) - 10001\(_{two}\)?...
Solve for (x, y) in the equation 2x + y = 4: x^2 + xy = -12...