Question

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Answer 1

The missing length $x=\frac{12}{5}$.

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.

⇒ $\frac{AB}{BC}= \frac{PQ}{QR}$

⇒ $\frac{4}{10}= \frac{x}{6}$

Do cross multiply.

⇒ $4 \times 6 = x \times 10$

⇒ $24 = 10x$

⇒ $x=\frac{24}{10}$

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

⇒ $x=\frac{12}{5}$

Hence, the missing length $x=\frac{12}{5}$.