Radical Expression

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Radical Expression

A ladder is placed against the wall of a building so that the base of the ladder is 5 feet from the bottom of the wall and the top of the ladder rests 15 feet up on the wall as shown in the figure. How long is the ladder? Leave your answer in simplified radical form
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Re: Radical Expression

A right triangle is formed.

Pythagorean Theorem
a² + b² = c²  {the sum of the squares of the legs is equal to the square of the hypotenuse}
a and b are the legs
c is the hypotenuse

5² + 15² = c²   {substituted into Pythagorean Theorem}
25 + 225 = c²   {evaluated exponents}
250 = c²   {added 25 and 225}
c = √250   {took square root of each side}
c= √25 √10   {broke down square root of 250}
c = 5√10   {evaluated square root of 25}

ladder is 5√10 ft

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