Question

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.

Answer 1

Answer:

The dimensions of the larger rectangle are $5\sqrt{6}\ in$ wide and $10\sqrt{6}\ in$ 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

$z^{2}=\frac{x}{y}$

we have

$y=5*10=50\ in^{2}$

$x=6y=6*50=300\ in^{2}$

substitute and solve for z

$z^{2}=\frac{300}{50}=6$

$z=\sqrt{6}$

therefore

The dimensions of the larger rectangle are

wide

$5\sqrt{6}\ in$

tall

$10\sqrt{6}\ in$