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taskmasters

Unfortunately, this item does not come with any figure to illustrate the lengths of the rectangle. However, it may be noted that by connecting two opposite vertices of a rectangle by a diagonal, we form a right triangle. We may then use the Pythagorean theorem to solve for the answer. 
                                     a² + b² = c²
c in this equation is the length of the diagonal, a and b are the lengths of the sides.

carlosego

For this case what we should do is define the variables.

We have then:

AB: length of the rectangle

BC: rectangle width

d: diagonal of the rectangle

The diagonal of the rectangle is given by:


\(d ^ 2 = AB ^ 2 + BC ^ 2
\)

From here, we clear the value of AB:

\(AB ^ 2 = d ^ 2 - BC ^ 2
\)

Substituting values:

\(AB ^ 2 = 2 ^ 2 - BC ^ 2

AB ^ 2 = 4 - BC ^ 2

AB = \sqrt{4 - BC ^ 2}\)

Answer:

the length of line segment AB is:

\(AB = \sqrt{4 - BC ^ 2}\)

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