Question

In rectangle ABCD, AC = 48 andBO = 5x + 4. What's the value of x?

A) 9



B) 4



C) 8



D) 8.8

Answer 1

B) 4

Explanation:

In a rectangle, the diagonals are equal in length and also bisect each other. Therefore, in the given rectangle ABCD:

• 
  `\overline{AC} = \overline{DB}`
• 
  `\overline{AO} = \overline{BO} = \overline{CO} = \overline{DO}`

Diagonal AC is the sum of segments AO and CO.

Since AO = BO = CO = DO, then AC = 2 · BO.

Therefore, given AC = 48 and BO = 5x + 4, then:

`\begin{aligned}\overline{AC} &= 2 \cdot \overline{BO}\\48 &= 2 \cdot (5x + 4)\\48 &= 10x + 8\\48 - 8 &= 10x + 8 - 8\\40 &= 10x\\10x &= 40\\10x / 10 &=40 / 10\\x &= 4\end{aligned}`

Therefore, the value of x is 4.