see the attached figure to better understand the problem
we have that

Step 1
<u>Find the value of AC</u>
we know that
in the right triangle ABC

substitute the values in the formula

Step 2
<u>Find the value of BC</u>
we know that
in the right triangle ABC
Applying the Pythagorean Theorem

substitute the values

Step 3
<u>Find the value of BD</u>
we know that
in the right triangle BCD
Applying the Pythagorean Theorem

substitute the values


therefore
<u>the answer is</u>
the length of BD is 11.93 units
3a - 4b = 21
check (-2 , -3)
3(-2) -4(-3) =21
-6 +12 = 21
6 does not = 21 so NO
check (0 , 7)
3(0) -4(7) =21
0-28=21
-28 does not equal 21 so NO
check (-3 , -2)
3(-3) -4(-2) =21
-9 +8 = 21
1 does not = 21 so NO
check (7 , 0)
3(7) -4(0) =21
21 = 21
Choice D
This is the Pythagorean theorem where the 2 legs of a triangle squared add up to equal the squared hypotenuse (a^2 + b^2 = c^2)
The equation would be
12^2 + 5^2 = x^2
144 + 25 = 169
The square root of 169 = 13
Answer - 13 ft