Calculate Triangle Perimeter: 15×8 Rectangle with Diagonal

To solve the problem of finding the perimeter of triangle ABD, we will apply the following steps:

• Step 1: Identify the given dimensions of the rectangle.
• Step 2: Calculate the length of the diagonal BD using the Pythagorean theorem.
• Step 3: Sum the sides of triangle ABD to find its perimeter.

Now, let's work through each step:

Step 1: We know from the problem that AB = 15 and AD = 8.

Step 2: The triangle ABD is a right triangle with AB and AD as the legs, and BD as the hypotenuse. Therefore, by the Pythagorean theorem:

$BD^2 = AB^2 + AD^2 = 15^2 + 8^2$

Calculating these squares gives:

$BD^2 = 225 + 64 = 289$

Taking the square root of both sides, we find:

$BD = \sqrt{289} = 17$

Step 3: Now, calculate the perimeter of triangle ABD.

$\text{Perimeter of ABD} = AB + AD + BD = 15 + 8 + 17 = 40$

Therefore, the perimeter of triangle ABD is $40$.