Question

If a stone tower is 15 meters tall and casts a shadow 8 meters long, then how long of a

shadow will be cast by a nearby radio tower that is 60 meters tall?

Answer 1

32 meters long (please double-check! sometimes ppl make mistakes)

Explanation:

the ratio of height to shadow length is 15:8, as established in the first sentence. if both sides of the ratio are multiplied by 4 then the ratio becomes 60:32.

more in depth:

if you think of it as fractions (which ratios can be written as) multiplying both the numerator and denominator by four is the equivalent of multiplying by 4/4 aka 1 so the value still stays the same (one times something is the same thing). since the ratio of height to shadow length is constant we needed to solve for the ratio in which the height is 60, so multiply each side by 4 (aka 60 divided by 15) to find the new ratio, 15(4):8(4) or 60:32. the ratio 60:32 describes height to shadow, so while the height is 60 (said in the problem) then the shadow length is 32. adding units, the answer would be 32 meters.