Question

This is geometry: The length of the hypotenuse of an isosceles right triangle is 30 meters. Find the area of the triangle. Round to the nearest tenth, if necessary.

Answer 1

Area of the triangle : A=(1/2)*base* height
in an right isosceles triangle, the base is one leg and the height is the other leg

Answer 2

A=(1/2)leg^2= (1/2)*(30/sqrt(2))^2=30^2/4

Answer 3

all you have to do is solve.

Answer 4

so just solve 30^2/4

Answer 5

and since the legs are the same you know
\[a^2+a^2=30^2\]
\[2a^2=30^2\]
\[a=\frac{30}{\sqrt{2}}\]

Answer 6

those are the lengths of the legs multiply them together and divide by two to get
\[\frac{1}{2}\times\frac{30^2}{2}=\frac{900}{4}=225\]