What is BC?

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2 Answers
marfre
Mar 21, 2018

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

Alan P.
Mar 21, 2018

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

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