Question

Find the area of a right isosceles triangle with hypotenuse 10\sqrt{2}10
2 units

Answer 1

Answer:

A = 50 square units

Step-by-step explanation:

Right Triangles

A right triangle is identified because it has one internal angle of 90°.

The longest side is called hypotenuse and the other two sides are called legs. Being c the hypotenuse and a and b the legs, the Pythagora's theorem relates the with the equation:

$c^2=a^2+b^2$

If the triangle is also isosceles, then both legs have the same measure or a=b:

$c^2=a^2+a^2=2a^2$

Since we know the hypotenuse has a measure of 10\sqrt{2}:

$(10\sqrt{2})^2=2a^2$

Operating:

$100*2=2a^2$

Dividing by 2:

$a^2=100~~\Rightarrow a=\sqrt{100}$

a = 10 units

The area of the triangle is:

$\displaystyle A=\frac{a.b}{2}$

$\displaystyle A=\frac{10*10}{2}$

A = 50 square units