One leg of an isosceles right triangle measures 5 inches. Rounded to the nearest tenth, what is the approximate length of the hypotenuse?
since it is isosceles right triangle, both legs = 5 inches.
using pythagoras theorem,
hypotenuse^2 = 5^2 +5^2 = 25+25 = 50
taking square root on both sides,
hypotenuse = sqrt 50 = 5 sqrt 2 or 7.071
rounded to nearest tenth,
length of hypotenuse is 7.1 inches.
The answer is 7.07 inch
The theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
From the given question , it is a isosceles right triangle
The base and perpendicular is given 5 inc.
By using Pythagoras theorem
\(h^{2} = p^{2} + b^{2} \\h^{2} = 5^{2} + 5^{2} \\h^{2} = 25 +25\\h^{2} = 50\\h = \sqrt{50} \\h = 7.07 inch\)
Therefore , the approximate length of the hypotenuse is 7.07 inch
learn more about Pythagoras theorem here:
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