Question

In the given trapezium ABCE, ED = 10 cm, DC = 15 cm, find the length of AB, if area of $△$ADE is one-third of area of trapezium ABCD.

• A. 2 cm
• B. 4 cm
• C. 5 cm
• D. 6 cm

Answer 1

The correct option is C 5 cm

According to condition
Area of $△$ADE
= $\frac{1}{3}$$\times$(area of trapezium ABCD)
$\frac{1}{2}$$\times$base$\times$height
=$\frac{1}{3}$$\times$$\frac{1}{2}$$\times$(sum of parallel sides)$\times$height

$\frac{1}{2}$$\times$ED$\times$AF = $\frac{1}{3}$$\times$$\frac{1}{2}$$\times$(AB+CE)$\times$AF
ED$\times$AF = $\frac{1}{3}$$\times$(AB+CE)$\times$AF

($\because$CE = ED + DC = 10 + 15 = 25 cm and
As heights (AF) are same for both)

ED = $\frac{1}{3}$$\times$(AB+25)
10 = $\frac{1}{3}$$\times$(AB+25)
10$\times$3 = AB+25
30 = AB+25
AB = 5 cm
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