Respuesta :
Answer:
the length of one leg of the triangle is, [tex] 5\sqrt{2}[/tex] inches
Step-by-step explanation:
In the special triangle 45-45-90 right isosceles triangle,
the ratio of sides to the hypotenuse of an isosceles triangle are:
[tex]a:a:a\sqrt{2}[/tex]
As per the statement:
The hypotenuse of an isosceles triangles measures 10 inches long.
⇒[tex]a\sqrt{2} = 10[/tex]
Divide both sides by [tex]\sqrt{2}[/tex] we have;
[tex]a = \frac{10}{\sqrt{2}} = 5\sqrt{2}[/tex]
⇒[tex]a= 5\sqrt{2}[/tex] inches
Therefore, the length of one leg of the triangle is, [tex] 5\sqrt{2}[/tex] inches
