The Area of EFGH is 2x+9 which is similar to The Area of JKLM is 2x-6. The perimeter of EFGH is x+3 which is similar to the Perimeter of JKLM is x-1. FInd all Possible values of X.

Step-by-step explanation:

Assume EFGH and JKLM are rectangles

JKLM appears to be the smaller of both.

So:

and

Where n is the scale of dilation

The area of EFGH is:

----- (1)

Substitute and

So, we have:

and

--- Given

--- Given

So:

and

and

Equate bot areas

Make n^2 the subject

The perimeter (P) of EFGH is:

----- (1)

Substitute and

So, we have:

and

--- Given

--- Given

So:

and

and

Equate bot perimeters

Make n the subject

Square both sides

Recall that:

So, we have:

Evaluate all squares

Cross multiply

Open brackets

Subtract 2x^3 from both sides

Collect like terms

Collect like terms

Expand

Factorize

x can not be negative.

So:

h= 12 inches

step-by-step explanation:

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