Question

The area of a trapezium of height $40\,\text{cm}$ is $1600\,\text{cm}^2$. One parallel side is $10\,\text{cm}$ longer than the other side. Find the ratio of the lengths of the parallel sides.

• A. $7:9$
• B. $5:7$
• C. $3:5$
• D. $2:3$

Hint:

For trapezium problems, the sum of parallel sides comes directly from \(\text{Area}=\tfrac{1}{2}(a+b)h\). Combine with any linear relation (like a difference) to solve quickly.

Answer 1

The Correct Option is A

Step 1: From the area formula, \( x+y=80 \) (sum of parallel sides), and from the given condition, \( y-x=10 \).

Step 2: Add the two equations: \( 2y=90 \Rightarrow y=45 \). Subtract them: \( 2x=70 \Rightarrow x=35 \).

Step 3: Ratio \( x:y=35:45=7:9 \). \[ \boxed{7:9} \]