What is the length of the ladder? The bottom of a ladder that is leaning against a building reaches 8 feet from the base of the
building. The top of the ladder reaches 15 feet up the side of the building. What is the length of
the ladder? Simplify if necessary.
275
Оа
Ob
17 Feet
289 Feet
23 Feet
Od

Step-by-step explanation:

a squared + b squared = c squared

8 squared + 15 squared = c squared

64 + 225 = c squared

289 = c squared

square root of 289 = c

17 = c

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!