SAT Question of the Day November 29th 2012

Miguel is 180 centimeters tall. At 2:00 p.m. one day, his shadow is 60 centimeters long, and the shadow of a nearby fence post is t centimeters long. In terms of t, what is the height, in centimeters, of the fence post?

A.     t + 120

B.     t over 3

C.     3 times t

D.     3 times (square root t)

E.     (t over 3)^2


When we read this question we notice that Miguel is 180 cm tall while is shadow is only 60 cm long (one third of his height). We are then given the length of an object’s shadow (t cm) and assuming it casts it’s shadow with the same RATIO to it’s height we are asked to express the object’s height in terms of t.

Now this might sound intimidating, however we are just asked to find the mathematical operation  that will allow us to calculate the height of an object given the length of the object’s shadow. With Miguel shadow we can calculate we need to multiply the length of his shadow (60 cm) times 3 in order to obtain his height (180 cm). Thus, we conclude that if this ratio is the same for any object, we need to multiply the length of the shadow (t) by 3 – to obtain 3t – which is the correct answer.

We can also look at this question as a ratio problem. 180 to 60 is the same as what to t? and again we conclude what we are looking for is 3t.


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