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Crazy boy [7]
3 years ago
14

Triangle K L J is cut by line segment N O. Line segment N O goes from side L K to side L J. The length of L N is (x minus 3) inc

hes, the length of N K is (x + 2) inches, the length of L O is (x minus 4) inches, and the length of O J is x inches. Which value of x would make Line segment N O is parallel to line segment K J? 1 6 8 10
Mathematics
2 answers:
kozerog [31]3 years ago
8 0

Answer: x= 8

Step-by-step explanation:

According to the converse of basic proportionality theorem,

If in ΔABC , DE is a line drawn from AB to AC such that \dfrac{AD}{DB}=\dfrac{AE}{EB}

then, DE is parallel to the third side BC.

Applying converse of basic proportionality theorem, to get NO parallel to KJ, we must have

\dfrac{LO}{OJ}=\dfrac{LN}{NK}\\\\\Rightarrow \dfrac{x-4}{x}=\dfrac{x-3}{x+2}\\\\\Rightarrow\ (x-4)(x+2)=x(x-3)\\\\\Rightarrow\ x^2-2x-8=x^2-3x\\\\\Rightarrow\ -2x+3x=8\\\\\Rightarrow\ x=8

Hence, the value of x should be 8, so that Line segment N O is parallel to line segment K J.

sukhopar [10]3 years ago
7 0

Answer:

Option C- 8

Explanation:

Plug it in- Hope this helps :)

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Answer:

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Step-by-step explanation:

<em>PART</em><em> </em><em>1</em><em> </em><em>:</em>

Area of rectangle = Length × Width

A = L × W

L = x - 3

W = x + 8

Therefore:

A = L × W

60 = ( x - 3 ) ( x + 8 )

( x - 3 ) ( x + 8 ) - 60 = 0

x^2 + 8x - 3x - 24 - 60 = 0

x^2 + 5x - 84 = 0

x^2 + 12x - 7x - 84 = 0

x ( x + 12 ) - 7 ( x + 12 ) = 0

( x + 12 ) ( x - 7 ) = 0

THEREFORE:

x = - 12 , x = 7

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

<em>PART</em><em> </em><em>2</em><em> </em><em>:</em>

L = x - 3

L = ( - 12 ) - 3

L = - 15

OR

L = ( 7 ) - 3

L = 4

THEREFORE:

Length can not be a negative number. Hence, L can not equal to - 15.

L = 4 inches

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

W = x + 8

W = ( 7 ) + 8

THEREFORE:

W = 15 inches

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