Question

ABCD is a trapezium. AD is parallel to BC.
AD is parallel to BC. AD= 2.1 m, AB= 1.9m, CD= 3.2m.
Work out the length of BC.

Answer 1

Step-by-step explanation:

Given:

1. ABCD is a trapezium.
2. AD is parallel to BC.
3. AD= 2.1 m,
4. AB= 1.9m,
5. CD= 3.2m.

To find: BC=?.

Construction: Draw line DE||AB.

Form construction: ABED is a parallelogram.

so, AD=BE=> 2.1m and AB=DE=> 1.9m.

Also, ∆CDE is right angled at E.

By Pythagorean triplet:

CD²=DE²+CE².

i.e., (3 2)²={1.9)²+EC².

=> 10.24-3.61=EC²

=> √6.63=EC

=> CE=2.5m(approx).

BC=BE+EC

=> 2.1+2.5

BC=4.6m.