Question

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Answer 1

The missing length
`x=(12)/(5)`.

Solution:

The image of the answer is attached below.

In figure ABCD, AB = 4, BC = 10

In figure PQRS, PQ = x, RS = 6

Given figures are similar.

If two figures are similar, then the sides are proportionate to each other.

⇒
`(AB)/(BC)= (PQ)/(QR)`

⇒
`(4)/(10)= (x)/(6)`

Do cross multiply.

⇒
`4 * 6 = x * 10`

⇒
`24 = 10x`

⇒
`x=(24)/(10)`

To reduce the length, divide both numerator and denominator by 2.

⇒
`x=(12)/(5)`

Hence, the missing length
`x=(12)/(5)`.