Question

For rectangle ABCD, if DC =16.4 ft and BC = 14.8 ft, find DB+AC

Answer 1

Recall that one property of a rectangle is that opposite sides are always equal.

Therefore, we can say that:

DC = AB

BC = AD

Because of this, we can also say that DB = AC.

Given:

DC = 16.4 ft.

BC = 14.8 ft.

Using the Pythagorean Theorem, let's find DB.

`\begin{gathered} \text{ c}^2=a^2+b^2 \\ \text{ DB}^2=DC^2+BC^2 \\ \text{ DB}^{}=√(DC^2+BC^2) \end{gathered}`
`\text{ DB = }\sqrt[]{16.4^2+14.8^2}\text{ = }\sqrt[]{268.96\text{ + 219.04}}`
`\text{ DB = }\sqrt[]{488}\text{ }\approx\text{ 22.1 ft.}`

Since DB = AC, DB + AC will be:

`\text{ DB + AC = DB + DB = 2DB}`
`\text{ 2(22.1) = 44.2 ft.}`

Therefore, DB + AC = 44.2 ft.

The answer is Choice B.