The hypotenuse of an isosceles triangles measures 10 inches long. What is the length of one leg of the triangle?

Answer:the length of one leg of the triangle is, [tex] 5\sqrt{2}[/tex] inchesStep-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] inchesTherefore, the length of one leg of the triangle is, [tex] 5\sqrt{2}[/tex] inches