Question

This is appicationof square roots

Answer 1

The area of the smaller square

`A_S=x^2`

The area of the larger square

`A_L=(2x)^2=4x^2`

The area of the larger square is 42cm² more than the smaller square.

Therefore we have the equation:

`A_L=A_S+42`

`4x^2=x^2+42\qquad|-x^2\\\\3x^2=42\qquad|:3\\\\x^2=14\to x=√(14)\ cm`

Answer:

`x=√(14)\ cm\approx3.7\ cm\\\\2x=2√(14)\ cm\approx7.5\ cm`