Question

100 Points! Geometry question. Photo attached. Please show as much work as possible. Only looking for an answer to question B. Thank you!

Answer 1

`\sf Scale \;factor=(√(71))/(4)`

`x=4.51\; \sf in\;(nearest\;hundredth)`

Explanation:

A scale factor is the number by which you multiply each side of a figure to enlarge or reduce it. If the scale factor is greater than 1, the figure is enlarged, and if the scale factor is between 0 and 1, the figure is reduced.

To calculate the area scale factor, divide the area of the new figure (image) by the area of the original figure (pre-image).

`\sf Area\;scale \;factor=(71\; in^2)/(16\;in^2)=(71)/(16)`

The length scale factor (standard scale factor) is calculated by taking the square root of the area scale factor.

`\sf Length\;scale \;factor=\sqrt{(71)/(16)} =(√(71))/(4)`

To find the value of x, divide the corresponding side length of the image by the (length) scale factor:

`x=9.5 / (√(71))/(4)=9.5 *(4)/(√(71))=(38√(17))/(17)\approx4.51\; \sf in\;(nearest\;hundredth)`