Question:
LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN = 3x + 1 and MP = 8x – 4
Answer:
Value of x = 9, Length of LN = 64, Length of MP = 64
Solution:
Given LMNP is a rectangle. LN and MP are diagonals.
LN = 5x + 19 and MP = 8x – 8
Diagonals of a rectangle are equal in length.
⇒ LN = MP
⇒ 5x + 19 = 8x – 8
Combine like terms together.
⇒ 19 + 8 = 8x – 5x
⇒ 27 = 3x
Divide by 3 on both sides of the expression, we get
⇒ x = 9
The value of x is 9.
To find the length of the diagonals.
LN = 5(9) + 19
= 45 + 19
LN = 64
MP = 8(9) – 8
= 72 – 8
MP = 64
Length of LN = 64 and the length of MP = 64.