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Reil [10]
3 years ago
15

A mailbox that is 36 inches tall is beside a tree.The length of the mailboxes shadow is 28 inches.The length of the trees shadow

is 98 inches.How tall is the tree in feet.
Mathematics
1 answer:
mixer [17]3 years ago
3 0

Answer:

10.5 feet

Step-by-step explanation:

In this problem, we have two similar triangles:

- One consists of the mailbox, its shadow and the hypothenuse

- The other one consists of the tree, its shadow and the hypothenuse

The two triangles are similar, so they have same proportions between their sides: therefore, we can apply the rule of three:

\frac{m}{s_m}=\frac{t}{s_t}

where

m = 36 in is the height of the mailbox

s_m=28 in is the shadow of the mailbox

t is the height of the tree

s_t=98 in is the length of the shadow of the tree

Solving for t, we find the height of the tree:

t=\frac{m\cdot s_t}{s_m}=\frac{(36)(98)}{28}=126 in

And since

1 feet = 12 inches

The height of the tree in feet is

t=\frac{126}{12}=10.5 ft

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