Question

use the diagram of a right isosceles triangle to answer the question.
diagram of a right isosceles triangle with legs marked equal, base 12 cm
what is the length of a leg of the triangle?
a. √6 cm
b. √12 cm
c. √36 cm
d. √72 cm
e. √142 cm

Explanation:

Step1: Recall Pythagorean theorem for right isosceles triangle

Let the length of each leg be \( x \). In a right isosceles triangle, the hypotenuse \( c \) and legs \( a = b = x \) satisfy \( a^2 + b^2 = c^2 \). So \( x^2 + x^2 = c^2 \), which simplifies to \( 2x^2 = c^2 \).

Step2: Substitute hypotenuse length

Given hypotenuse \( c = 12 \) cm. Substitute into the equation: \( 2x^2 = 12^2 \).

Step3: Solve for \( x^2 \)

Simplify \( 12^2 = 144 \), so \( 2x^2 = 144 \). Divide both sides by 2: \( x^2 = \frac{144}{2} = 72 \).

Step4: Solve for \( x \)

Take square root of both sides: \( x = \sqrt{72} \) (since length is positive).

Answer:

D. \(\sqrt{72}\) cm