Question

find the perimeter and area of the triangle. (the figure is not shown to scale.) the perimeter of the triangle is blank (triangle with legs 60, 11 and hypotenuse 61, right-angled)

Explanation:

Step1: Recall perimeter formula for triangle

The perimeter \( P \) of a triangle is the sum of its three side lengths. For this right triangle, the side lengths are \( 11 \), \( 60 \), and \( 61 \).
\[
P = 11 + 60 + 61
\]

Step2: Calculate the sum

First, add \( 11 \) and \( 60 \): \( 11 + 60 = 71 \). Then add \( 71 \) and \( 61 \): \( 71 + 61 = 132 \).

For the area, the formula for the area \( A \) of a right triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \). Here, the base can be \( 11 \) and the height \( 60 \) (or vice versa).

Step3: Calculate the area

\[
A = \frac{1}{2} \times 11 \times 60
\]
First, multiply \( 11 \) and \( 60 \): \( 11 \times 60 = 660 \). Then multiply by \( \frac{1}{2} \): \( \frac{1}{2} \times 660 = 330 \).

Answer:

The perimeter of the triangle is \( 132 \), and the area of the triangle is \( 330 \).