Question

Given rectangle ABCD, AC = 7x - 2, DE = 3x + 1. Find DB

Answer 1

DB=26 units

Step-by-step explanation:

In rectangle ABCD

• AC=7x-2

,

• DE = 3x+1

The diagonals of a rectangle are equal and bisect each other.

Thus, it implies that:

`DE=(1)/(2)AC`

Substituting the given values:

`\begin{gathered} 3x+1=(1)/(2)(7x-2) \\ 2(3x+1)=7x-2 \\ 6x+2=7x-2 \\ 2+2=7x-6x \\ x=4 \end{gathered}`

Since the diagonals are equal:

`\begin{gathered} DB=AC \\ AC=7x-2 \\ =7(4)-2 \\ =28-2 \\ =26\text{ units} \\ \implies DB=26\text{ units} \end{gathered}`

The length of DB is 26 units.