Question

To the nearest tenth, what is the length of the hypotenuse of an isosceles right triangle with a leg of 7 square root 3 inches?

Answer 1

To find the length of the hypotenuse of an isosceles right triangle, we can use the Pythagorean theorem. In this case, the length of one leg is 7 square root 3 inches. By substituting this value into the Pythagorean theorem equation and solving for the hypotenuse, we find that it is approximately 14.5 inches.

Step-by-step explanation:

The length of the hypotenuse of an isosceles right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two legs. In this case, one leg has a length of 7√3 inches. Let's call the length of the other leg x inches. Using the Pythagorean theorem, we have:

x^2 + (7√3)^2 = x^2 + 63 = c^2

where c represents the length of the hypotenuse. To find c, we take the square root of both sides:

√(x^2 + 63) = c

Since it is an isosceles right triangle, the length of both legs is the same. Therefore, x = 7√3. Substituting this value into the equation, we have:

√((7√3)^2 + 63) = √(147 + 63) = √210 = 14.5 inches (to the nearest tenth)

Answer 2

if it's a right triangle, and is also an isosceles triangle, namely two sides are of equal length, that means the other non-right-angles are 45° each, so the triangle is a 45-45-90 triangle, and thus we can apply the 45-45-90 rule, so let's do so. Check the picture below.