Answer:
70.74in
Explanation:
So first lets break this shape into two parts, a rectangle, and a triangle.
Lets find the perimeter of the rectangle, equation 2(l+w):
l = 17
w = 10
2(17+10) = 54
the perimeter of the rectangle is 54in
Now lets find the perimeter of the triangle, equation a+b+c
a = x
b = 4
c = 7
we don't know the length of one side, but we can use the Pythagorean theorem to find it.
a^2 + b^2 = c^2
x^2 + 4^2 = 7^2
x^2 + 16 = 49
x^2 = 33
x = 5.74
a = 5.74
b = 4
c = 7
now lets plug it into our equation
p = a + b + c
p = 5.74 + 4 + 7
p = 16.74
We have both the perimeter of the rectangle, 54, and the triangle, 16.74, now we add them up to find the perimeter of the entire shape.
54 + 16.74 = 70.74