Question

If JKLM is a rectangle, JL = 2x + 5, and MK = 7x – 40, find MK

Answer 1

Answer:

MK = 23

Step-by-step explanation:

Rectangle means that the angles are all 90 degrees, so all the sides are not tilted in any direction. Meaning the JL = MK, therefore:

2x + 5 = 7x - 40

subtract 5 from both sides

2x = 7x - 45

subtract 7x from both sides

-5x = -45

divide by -5

x = 9

Now input 9 into the equation

MK = 7(9) - 40 = 63 - 40 = 23

Answer 2

The value of MK is 23.

• We would need to apply our knowledge of the property of rectangles to solve the given problem.

• Recall:

The diagonals of a rectangle that intersect each other are equal (a property of a rectangle).

• Thus:

$JL = 2x + 5 (given)\\\\MK = 7x - 40 (given)$

Therefore:

• $JL = MK$ (diagonals of rectangle JKLM)

• Substitute

$2x + 5 = 7x - 40$

• Collect like terms

$2x -7x = -5-40\\\\-5x = -45$

• Divide both sides by -9

$x = 9$

• Find $MK$:

$MK = 7x - 40$

• Plug in the value of x

$MK = 7(9) - 40\\\\MK = 63 - 40\\\\MK = 23$

• Therefore, the value of MK is 23.

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