Question

find the lengths of the diagonals of RT as 3m+2 and 4m-3 and SU 2n+2 and 8+n

Answer 1

To find the lengths of the diagonals \( RT \) and \( SU \) based on the given expressions, we can set the two expressions for each diagonal equal to each other since the lengths of the diagonals must be the same.

**For diagonal RT:**
1. Set \( 3m + 2 = 4m - 3 \).
2. To solve for \( m \):
- Subtract \( 3m \) from both sides:
\[
2 = m - 3
\]
- Add \( 3 \) to both sides:
\[
m = 5
\]
3. Substitute \( m = 5 \) back into either expression to find the length of \( RT \):
- Using \( 3m + 2 \):
\[
RT = 3(5) + 2 = 15 + 2 = 17
\]

**For diagonal SU:**
1. Set \( 2n + 2 = 8 + n \).
2. To solve for \( n \):
- Subtract \( n \) from both sides:
\[
2n - n + 2 = 8
\]
\[
n + 2 = 8
\]
- Subtract \( 2 \) from both sides:
\[
n = 6
\]
3. Substitute \( n = 6 \) back into either expression to find the length of \( SU \):
- Using \( 2n + 2 \):
\[
SU = 2(6) + 2 = 12 + 2 = 14
\]

Thus, the lengths of the diagonals are:
- Length of diagonal \( RT \) is \( 17 \, m \)
- Length of diagonal \( SU \) is \( 14 \, m \)