Question

what is the value of p? triangle image with right angle, two 45° angles, base 44, side p options: p = 22; p = 44; p = 22√2; p = 44√3

Explanation:

Step1: Identify triangle type

This is a right isosceles triangle (90° + 45° + 45°), so the two legs (length $p$) are equal, and the hypotenuse is 44.

Step2: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$. Here $a = b = p$, $c = 44$.
$$p^2 + p^2 = 44^2$$

Step3: Simplify the equation

Combine like terms and solve for $p$.
$$2p^2 = 1936$$
$$p^2 = \frac{1936}{2} = 968$$
$$p = \sqrt{968} = \sqrt{484 \times 2} = 22\sqrt{2}$$

Answer:

$p = 22\sqrt{2}$ (Option 3)