Question

Parallelograms:
ABCD∼A1B1C1D1.
Find BC, B1D1

Answer 1

`BC = 4.8` and
`B_(1)D_(1) = 6.25`

Explanation:

The parallelograms ABCD and
`A_(1) B_(1) C_(1)D_(1)` are similar.

Now, AB = 8 (Given in the figure), so CD = 8.

Now, we can write,
`(BC)/(B_(1)C_(1))  = (CD)/(C_(1)D_(1))`

⇒
`(BC)/(3) = (8)/(5)`

{Since, given that
`B_(1)C_(1) = 3` and
`C_(1)D_(1) = 5`}

⇒
`BC = (8 * 3)/(5) = 4.8` (Answer)

Again, we can write,
`(BD)/(B_(1)D_(1))  = (CD)/(C_(1)D_(1))`

⇒
`(10)/(B_(1)D_(1)) = (8)/(5)` {Since, BD = 5 + 5 = 10}

⇒
`B_(1)D_(1) = (5 * 10)/(8) = 6.25` (Answer)