Question

if the legs of a 45degree -45 degree -90 degree triangle have a length of 8 centimeters, what is the perimeter of the triangle

Answer 1

By Pythagorean Theorem
\[a ^{2}+b ^{2}=c ^{2}\]
\[8^{2}+8^{2}=c ^{2}\]
\[64+64=c ^{2}\]
\[c=\sqrt{128}=8\sqrt{2}\]
\[P=8+8+8\sqrt{2}=16+8\sqrt{2}\]

Answer 2

For 45degree -45 degree -90 degree triangle there is a short cut
if the leg is length a, the hypotenuse is length a*sqrt(2)

so the perimeter is 2a+a*sqrt(2) . in this case, a=8, so 16+8*sqrt(2)

Answer 3

Yes, you got it