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The hypotenuse and a leg of a particular right triangle are \(\sqrt97\) inches and 4 inches, respectively. The area of this triangle is what common fraction of a square foot?

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 May 15, 2020
edited by Guest  May 15, 2020
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area of triangle   =   \(\frac12\)  *  base  *  height

 

We know the base is  4 inches.  To find the height we can use the Pythagorean theorem.

 

42  +  h2   =   √[ 97 ]2

 

16  +  h2   =   97

 

h2   =   81

 

h   =   9

 

The height is  9  inches.

 

base   =   4 inches   =   4/12  feet   =   1/3  feet

 

height   =   9 inches   =   9/12 feet   =   3/4 feet

 

area of triangle   =   \(\frac12\cdot\frac13\cdot\frac34\ \)   sq feet   =   \(\frac18\)  sq feet

 May 15, 2020

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