Answer:
length of the legs is [tex]5\sqrt{2}[/tex]
Step-by-step explanation:
the both sides of the length of the legs of a right triangle are equal
So it form a isosceles triangle 45- 45- 90 degree triangle
the ratio of 45-45-90 degree triangle is [tex]x:x:x\sqrt{2}[/tex]
xsqrt(2) is the side opposite to 90 degree
so [tex]hypotenuse =x\sqrt{2}[/tex]
[tex]10=x\sqrt{2}[/tex]
Divide both sides by square root (2)
[tex]\frac{10}{\sqrt{2}}=x[/tex]
multiply square root (2) at the top and bottom
[tex]\frac{10 \cdot \sqrt{2}}{2}=x[/tex]
[tex]x=5\sqrt{2}[/tex]
length of the legs is [tex]5\sqrt{2}[/tex]
