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Taya2010 [7]
3 years ago
6

TOVOU, V V VI VIOLIIV VYVI

Mathematics
1 answer:
Vaselesa [24]3 years ago
3 0

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.

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