Question

1. abcd is a rectangle. find the length of each diagonal. ac = 2(5a + 1) bd = 2(a + 1)

Explanation:

Step1: Equate diagonals

In a rectangle, the diagonals are equal. So, $AC = BD$.
$2(5a + 1)=2(a + 1)$

Step2: Divide both sides by 2

Dividing both sides of the equation by 2 simplifies it.
$5a + 1=a + 1$

Step3: Subtract a from both sides

Isolate the variable terms.
$5a - a+ 1=a - a + 1$
$4a+1 = 1$

Step4: Subtract 1 from both sides

Get the term with a alone on one side.
$4a+1 - 1=1 - 1$
$4a = 0$

Step5: Solve for a

Divide both sides by 4.
$a=\frac{0}{4}=0$

Step6: Find the length of the diagonal

Substitute a = 0 into the expression for either diagonal. Let's use the expression for BD.
$BD=2(a + 1)=2(0 + 1)=2$

Answer:

2