Question

A tree with a height of 12 yards casts a shadow that is 33 yards long at a certain time of day. At the same time, another tree nearby casts a shadow that is 20 yards long. How tall is the second tree?

Answer 1

Answer: Height of second tree would be 7.27 yards.

Step-by-step explanation:

Since we have given that

Height of a tree = 12 yards

Length of shadow of tree = 33 yards

If the shadow of tree = 20 yards

Then, we need to find the height of tree.

Since there is direct relation between height of tree and length of its shadow.

So, Let the height of tree in the second case be 'x'.

So, it becomes,

$\dfrac{12}{33}=\dfrac{x}{20}\\\\\dfrac{12\times 20}{33}=x\\\\7.27\ yards=x$

Hence, height of second tree would be 7.27 yards.

Answer 2

$Shadow\ of\ second\ three\ is\\\\ 33+20=53\\ Triangles\ made\ of\ three\ and\ shadows\ are\ similar, so\\ Proportion\ of\ length\ of\ shadow:\ \frac{53}{33}\\\\ Height\ will\ be\ on\ the\ same\ proportion\\\\ \frac{x}{12}=\frac{53}{33}\\\\ 3x=53*12\\ 3x=636\\ x=212\\ Second\ three\ has\ 212\ yards.$