A right isosceles triangle has an area of 18. What is the length of the longest side of the triangle?

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Answer 1 · 2017-02-03T10:51:39

#"The Desired Length"=6sqrt2" units."#

Consider a Right Isosceles #DeltaABC# with, #AB=BC#

Clearly, #m/_B=90^@,# so that, #AC# being the Hypotenuse is

the longest side of #Delta ABC.#

Now, the Area of #Delta ABC=1/2xxABxxBC#

#=1/2AB^2, .........[because, AB=AC]#.

#:. Area =18 rArr 1/2AB^2=18 rArr AB^2=36=BC^2.#

Using Pythagoras' Theorem, in #Delta ABC#, we have,

#AB^2+BC^2=AC^2=36+36=72#

#:. AC=sqrt72=6sqrt2# is the desired lemgth.