Question

what is the length of each leg of the triangle below?
a. 13
b. \\( \sqrt { 13 } \\)
c. 1
d. \\( 13 \sqrt { 2 } \\)
e. 18
f. \\( \sqrt { 26 } \\)

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right triangle. In a 45 - 45 - 90 triangle, the legs are equal, and the hypotenuse \( c \) is related to the leg length \( l \) by the formula \( c = l\sqrt{2} \), or \( l=\frac{c}{\sqrt{2}} \).

Step2: Substitute the hypotenuse value

Given the hypotenuse \( c = 26 \). We need to find the leg length \( l \). Using the formula \( l=\frac{c}{\sqrt{2}} \), substitute \( c = 26 \):

$$ l=\frac{26}{\sqrt{2}} $$

Step3: Rationalize the denominator

Multiply the numerator and denominator by \( \sqrt{2} \) to rationalize:

$$ l=\frac{26\sqrt{2}}{2}=13\sqrt{2} $$

Answer:

D. \( 13\sqrt{2} \)