Question

What is BC?

Answer 1

`BC = 10; " "BE = sqrt(149)/2~~6.10`

Explanation:

Given: A rectangle, `AD = 10; CD = 7`

Some properties of rectangles:
Opposite sides are parallel and congruent:
`AB = CD; BC = AD; " " **BC = 10**`

The length of the diagonals are congruent: `AC = BD`

The place where the diagonals cross is the midpoint or half-way point: `BE = 1/2AC = 1/2 BD`

The four corners are right angles. This means we can use the Pythagorean Theorem:
`(AC)^2 = (AD)^2 + (CD)^2`

`AC = BD = sqrt((AD)^2 + (CD)^2) = sqrt(10^2 + 7^2)`

`AC = BD = sqrt(100 +40) = sqrt(149) ~~12.21`

`BE = 1/2 AC = sqrt(149)/2 ~~6.10`

Answer 2

`abs(BC)=10`

Explanation:

We are told that `ABCD` is a rectangle.
Opposite sides of a rectangle are the same length.
Therefore `abs(BC)=abs(AD)`
and
we are told that `abs(AD)=10`
Therefore `abs(BC)=10`