Question

Examine rectangle JKLM, shown below.

If JN=x+3 and JL 3x + 1, determine which of the following values is correct

Answer 1

Answer:NM=8

Step-by-step explanation:

JN is half of JL so x + 3 times 2 is equal to 3x + 1

then u just do the work

2x+6=3x+1

5=x

then you just plug in the answers and JN is equal to 8 therefore NM is also equal to 8

Answer 2

To solve the problem we must know about the properties of the diagonals of a rectangle.

What are the properties of the diagonals of a rectangle?

• The diagonals of a rectangle are of equal length.
• The diagonals of the rectangle bisect each other at equal distances.

The correct statement from all the given options is D.

Given to us

JN = x+3

JL = 3x+1

What is the value of x?

We know that the diagonals of the rectangle bisect each other at two equal parts, therefore, JN=NL, also

$JL = JN + NL\\\\\text{Substituting the values,}\\\\3x+1 = x+3 + NL\\\\3x+1 = x+3 + NL\\\\3x-x=3-1+NL \ \ \ \ \ [JN=NL]\\\\2x = 2 + JN\\\\2x = 2 + x+3\\\\2x-x=5\\\\x = 5$

Value of diagonals

As we know the values of the diagonals are equal, therefore,

JL = KM = 3x + 1

JL = KM = 3(5) + 1

JL = KM = 16

Value of half Diagonals

We know that the diagonals of the rectangle bisect each other at two equal parts, also the diagonal are equal therefore all the four parts of the two diagonals will be equal.

JN = NL = KN = NM = x+3

JN = NL = KN = NM = 5+3

JN = NL = KN = NM = 8

Hence, the correct statement from all the given options is D.

Learn more about Diagonals:

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