The hypotenuse is 10 and the area is 24, how do you find the other lengths on the triangle?

1 Answer
Özgür Özer
Dec 29, 2015

6 and 8.

Explanation:

Let the other side lengths be a and b and area be A. Then,
color(white)xxA=24
=>(ab)/2=24color(white)(xxxxxxxxxxxxxxxx)(area formula)
=>2ab=96color(white)(xxxxxxxxxxxxxxxx)

=>a^2+b^2=100color(white)(xxxxxxxxxxxxx)(The Pythagorean Theorem)

=>a^2+b^2color(red)(+2ab)=100color(red)(+2ab)color(white)(xxxxxxxxxxxxx)
=>(a+b)^2=100+96color(white)(xxxxxxxxx)(A fundamental identity)
=>a+b=sqrt196color(white)(xxxxxxxxx)
=>a+b=14color(white)(xxxxxxxxx)

The two number, of which product is 48 and sum is 14, are 6 and 8.
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