Question

what is the perimeter, in feet, of the isosceles right triangle show below? 11 45° 45°

Explanation:

Step1: Determine the length of the other leg

Since it is an isosceles right - triangle, the two legs are equal. One leg is \(11\) feet, so the other leg is also \(11\) feet.

Step2: Calculate the length of the hypotenuse

Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\) (where \(a = b=11\)).

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Step3: Calculate the perimeter

The perimeter \(P=a + b + c\), with \(a = 11\), \(b = 11\) and \(c=11\sqrt{2}\).

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Answer:

\(22 + 11\sqrt{2}\) feet