The photograph of a house occupies an area of 1.75 cm² on a 35 mm slide. The slide is projected on to a screen and the area of the house-on the screen is 1.55 m². What is the linear magnification of the projector-screen arrangement?

To find the linear magnification of the projector-screen arrangement, we need to understand the relationship between area magnification and linear magnification.

First, let's identify the given values:
Area of the house on the slide, $A_{\text{slide}}=\; 1.75\backslash text\{\; cm\}^2$
Area of the house on the screen, $A_{\text{screen}}=\; 1.55\backslash text\{\; m\}^2$

Next, we must convert both areas to the same unit. Let's convert the screen area from square meters (${\text{m}}^2$) to square centimeters (${\text{cm}}^2$).
Since $\mathrm{1\backslash text\{\; m\}\; =\; 100\backslash text\{\; cm\}}$, we have:
$\mathrm{1\backslash text\{\; m\}^2\; =\; (100\backslash text\{\; cm\})^2\; =\; 10,000\backslash text\{\; cm\}^2\; =\; 10^4\backslash text\{\; cm\}^2}$

Thus, the area on the screen is:
$A_{\text{screen}}=\; 1.55\; \backslash times\; 10^4\backslash text\{\; cm\}^2\; =\; 15,500\backslash text\{\; cm\}^2$

The area magnification ($m_A$) is defined as the ratio of the image area on the screen to the object area on the slide:
$m_A=\; \backslash frac\{\backslash msub>A\text{screen}\}\{\backslash msub>A\text{slide}\}$

Substitute the values into the formula:
$m_A=\; \backslash frac\{15,500\}\{1.75\}\; \backslash approx\; 8857.14$

Linear magnification ($m$) is the ratio of the linear dimensions of the image to the object. It is related to area magnification by the following relation:
$m_A=\; m^2$

Therefore, the linear magnification is the square root of the area magnification:
$m$
$m$

Rounding to one decimal place, the linear magnification of the arrangement is 94.1.