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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