Question

abcd is a rectangle. find the length of each diagonal. ac = 2(x - 2) and bd = x + 6. ac = , bd =

Explanation:

Step1: Recall property of rectangle diagonals

In a rectangle, the diagonals are equal. So, $AC = BD$.
$2(x - 2)=x + 6$

Step2: Expand the left - hand side

Using the distributive property $a(b - c)=ab - ac$, we have $2x-4=x + 6$.

Step3: Isolate the variable $x$

Subtract $x$ from both sides: $2x-x-4=x - x+6$, which simplifies to $x-4 = 6$.

Step4: Solve for $x$

Add 4 to both sides: $x-4 + 4=6 + 4$, so $x = 10$.

Step5: Find the length of $AC$

Substitute $x = 10$ into the expression for $AC$: $AC=2(x - 2)=2(10 - 2)=2\times8 = 16$.

Step6: Find the length of $BD$

Since $AC = BD$, $BD=x + 6=10+6 = 16$.

Answer:

$AC = 16$, $BD = 16$