Question

select the correct answer. abcd is a rectangle. the length of $overline{ac}$ is $4x - 8$, and the length of $overline{bd}$ is $2x + 10$. what is the length of one of its diagonals?

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal. So, $AC = BD$. That is, $4x - 8=2x + 10$.

Step2: Solve for x

Subtract $2x$ from both sides: $4x-2x - 8=2x-2x + 10$, which simplifies to $2x-8 = 10$. Then add 8 to both sides: $2x-8 + 8=10 + 8$, getting $2x=18$. Divide both sides by 2: $x = 9$.

Step3: Find diagonal length

Substitute $x = 9$ into the expression for either diagonal. Using the expression for $BD$ (we could also use $AC$), $BD=2x + 10$. So, $BD=2\times9+10=18 + 10=28$.

Answer:

28