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Abcd is rectangle find the length of each diagonal when AC=(y+c) ,BD=(3y-4)

Sagot :

Ashulav2005idn

Answer:

To find the length of each diagonal of the rectangle ABCD, you can use the property that in a rectangle, the diagonals are equal in length. This means that:

\[

AC = BD

\]

Given:

- \( AC = y + c \)

- \( BD = 3y - 4 \)

Since the diagonals are equal:

\[

y + c = 3y - 4

\]

Now, solve for \( y \):

1. Subtract \( y \) from both sides:

\[

c = 2y - 4

\]

2. Add 4 to both sides:

\[

c + 4 = 2y

\]

3. Divide by 2:

\[

y = \frac{c + 4}{2}

\]

Now that you have \( y \), you can substitute it back into the expression for \( AC \) or \( BD \) to find the length of the diagonal.

Using \( AC = y + c \):

\[

AC = \frac{c + 4}{2} + c

\]

Simplifying:

\[

AC = \frac{c + 4 + 2c}{2} = \frac{3c + 4}{2}

\]

So, the length of each diagonal is \( \frac{3c + 4}{2} \).

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