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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