The perimeter of a figure is the sum of all of its sides.
In this case, we need to find the length of the missing side before we calculate the perimeter.
Step 1. Draw a right triangle inside the figure with the missing side as the hypotenuse:
The blue sides are the legs of the triangle, and the red side, the missing side of the figure, is the hypotenuse.
Step 2. Find the lengths of the blue sides of the triangle:
The vertical side is equal to 10in - 6 in because of the given lengths, so the vertical side is:
[tex]10in-6in=4in[/tex]
And the horizontal side:
[tex]15in-7in-5in=3in[/tex]
Step 3. Use the Pythagorean theorem to find the missing side of the triangle.
According to the Pythagorean theorem, the hypotenuse (which we will call "x") squared is equal to the sum of the legs squared:
[tex]x^2=4^2+3^2[/tex]
Solving the operations:
[tex]\begin{gathered} x^2=16+9 \\ x^2=25 \end{gathered}[/tex]
Now, take the square root of both sides of the equation:
[tex]\begin{gathered} \sqrt[]{x^2}=\sqrt[]{25} \\ x=5 \end{gathered}[/tex]
The missing side is 5:
Step 4. Calculate the perimeter by adding all of the sides:
[tex]5in+7in+6in+5in+10in+15in=48in[/tex]
Answer: 48 in
