Find lopl in the figure below

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to find the length of OP using the Pythagorean theorem.

Identify the knowns and the unknown in the right-angled triangle.
The triangle has a right angle at O.
The length of side OQ is $2 \text{ cm}$ .
The length of the hypotenuse QP is $4 \text{ cm}$ .
We need to find the length of side OP.
Apply the Pythagorean theorem.
The Pythagorean theorem states that $a^2 + b^2 = c^2$ , where $a$ and $b$ are the lengths of the two shorter sides and $c$ is the length of the hypotenuse.
In this triangle:
$OQ^2 + OP^2 = QP^2$
Substitute the known values into the equation.
$(2 \text{ cm})^2 + OP^2 = (4 \text{ cm})^2$ $4 \text{ cm}^2 + OP^2 = 16 \text{ cm}^2$
Solve for $OP^2$ .
$OP^2 = 16 \text{ cm}^2 - 4 \text{ cm}^2$ $OP^2 = 12 \text{ cm}^2$
Find the length of OP by taking the square root.
$OP = \sqrt{12 \text{ cm}^2}$ $OP = \sqrt{4 \times 3} \text{ cm}$ $OP = 2\sqrt{3} \text{ cm}$
The length of OP is $2\sqrt{3} \text{ cm}$ .

Answer