Question

what is the length of the hypotenuse in the triangle shown?

Explanation:

Step1: Determine the lengths of the two legs

From the grid, we can see that the lengths of the two legs of the right - triangle are \(a = 3\) and \(b = 4\) (by counting the number of units on the grid).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the length of the hypotenuse. Substitute \(a = 3\) and \(b = 4\) into the formula:

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Step3: Solve for \(c\)

Take the square root of both sides of the equation \(c^{2}=25\). Since \(c>0\) (length cannot be negative), \(c=\sqrt{25}=5\)

Answer:

\(5\)