Given AD . AD = 24, BC = 12, AB = CD. a) Find AB. b) Find BD.

Answer 1

I'm assuming AD is a line segment with B and C plotted along the segment between A and D:

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A B C D

Given:

The entire line from A to D = 24

The distance from B to C = 12

AB = CD

12

l------------------------------l

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A B C D

l----------------------------------------------------------------------------l

24

Subtract 24 - 12 and this leaves 12 to be split between line segments AB and CD. Since these are given to be equal to each other, the left over 12 divided by 2 is equal to 6, so AB and CD each equal 6:

6 12 6

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A B C D

So AB = 6

and BD = 18

Answer 2

It's a parallelgram. If you knew its height, you could calculate the missing sides

Let h= the height. Without more information, the height could be any number.

AB is the hypotenuse of a right triangle with sides 6 and h, so AB^2 = 36 + h^2

and AB = sqr(36+h^2)

BD is a diagonal across the parallelogram. and is the hypotenuse of a right triangle with sides 18 and h.

BD^2 = 18^2 + h^2

BD = sqr(324+h^2)