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In a certain isosceles right triangle, the altitude to the hypotenuse has length \(4\sqrt2\). What is the area of the triangle?

Guest Jun 16, 2018
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drawing the triangle and setting the two equal sides as x and the height is 4sqrt2

 

we see that the height splits the 90 degree angle into two 45 degree angles and makes a 90 degree angle at the base

 

now we can use sin of o/h or sin 45 = 4sqrt2 / x which gives us x = 8

 

now we can use pythagorean to see that 8^2+ 8^2 = B^2 or the base is 11.3

 

now we apply the area formula bh/2 for area.

 

4sqrt2 * 11.3 = 64/2 = 32 so area is 32

Guest Jun 16, 2018

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