Aladder is leaning against a building the base of the ladder is 6 feet from the building and the top of the letter rests on the building 8 feet above the ground what is the length, in feet of the ladder

Remark

This is an application of the Pythagorean Theorem. The formula you will be using is a^2 + b^2 = c^2 and you are looking for c

Givens

a = 6

b = 8

c = ??

Sub and solve

a^2 + b^2 = c^2

6^2 + 8^2 = c^2

36 + 64 = c^2

100 = c^2

sqrt(c^2) = sqrt(100)

c = 10

The length of the ladder is 10 feet.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

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