A Partridge in a Pear Tree

Algebra Level 1

A man would like to go up a pear tree which is 20 feet high. He places a ladder against it so that the top of the ladder rests against the top of the tree and the base of the ladder is 15 feet from the base of the tree. How long (in feet) is the ladder?

Really Long 625 feet 25 feet 24 feet 576 feet

1 solution

Angela Fajardo
Dec 28, 2015

Using the Pythagorean Theorem: ${ a }^{ 2 } + { b }^{ 2 } = { c }^{ 2 }$

let:

 a = height of the tree

 b = distance of ladder from the tree

 c = length of the ladder

${ a }^{ 2 } + { b }^{ 2 } = { c }^{ 2 }$

Substitute the values in the Pythagorean Theorem.

${ 20 }^{ 2 }+{ 15 }^{ 2 } = { c }^{ 2 }$

Do the Exponents.

$400+{ 225={ c }^{ 2 } }$

Add.

${ 625={ c }^{ 2 } }$

Square Root both sides.

$\sqrt { 625 } { ={ \sqrt { c^{ 2 } } } }$

Now we have the value of c.

$25\quad =\quad c$

So, the answer is 25 feet.

A Partridge in a Pear Tree

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