Question

Can someone please answer 5, 6 and 7? Thank you.

Answer 1

Reduce a 24 cm by 36 cm photo to 3/4 original size.

The most logical way to do this is to keep the width-to-height ratio the same:  It is 24/36, or 2/3.  The original photo has an area of (24 cm)(36 cm) = 864 cm^2.

Let's reduce that to 3/4 size:  Mult. 864 cm^2 by (3/4).  Result:  648 cm^2.

We need to find new L and new W such that W/L = 2/3 and WL = 648 cm^2.

From the first equation we get W = 2L/3.  Thus, WL = 648 cm^2 = (2L/3)(L).

Solve this last equation for L^2, and then for L:

2L^2/3 = 648, or (2/3)L^2 = 648.  Thus, L^2 = (3/2)(648 cm^2) = 972 cm^2.

Taking the sqrt of both sides, L = + 31.18 cm.  Then W must be 2/3 of that, or W = 20.78 cm.

Check:  is LW = (3/4) of the original 864 cm^2?  YES.