To find the value of x and the length of each diagonal without using the Pythagorean theorem, we can use the fact that opposite sides of a rectangle are equal in length.
Since LMNP is a rectangle, LN must be equal in length to MP:
7x + 6 = 9x - 2
Subtract 7x from both sides:
6 = 2x - 2
Add 2 to both sides:
8 = 2x
Divide by 2:
x = 4
Now that we know that x = 4, we can substitute it back into the expressions for LN and MP to find their lengths:
LN = 7(4) + 6 = 34
MP = 9(4) - 2 = 34
Therefore, the value of x is 4 and the length of each diagonal is 34.
LMNP is a rectangle. find the value of x and the length of each diagonal.
LN = 7x + 6
MP = 9x - 2
find the answer without Pythagorean theorem
1 answer
1 answer