A rectangular picture frame is 5 inches wide and 10 inches tall. You want to make the area 6 times as large by increasing the length and width by the same amount. Find the number of inches by which each dimension must be increased.

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calculista calculista · Answer 1 · 2019-03-05T01:23:32+01:00

Answer:

The dimensions of the larger rectangle are [tex]5\sqrt{6}\ in[/tex] wide and [tex]10\sqrt{6}\ in[/tex] tall

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z------> the scale factor

x----> the area of the larger rectangle

y----> the area of the original rectangle

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]y=5*10=50\ in^{2}[/tex]

[tex]x=6y=6*50=300\ in^{2}[/tex]

substitute and solve for z

[tex]z^{2}=\frac{300}{50}=6[/tex]

[tex]z=\sqrt{6}[/tex]

therefore

The dimensions of the larger rectangle are

wide

[tex]5\sqrt{6}\ in[/tex]

tall

[tex]10\sqrt{6}\ in[/tex]