SOLUTION: HIJK and STUV are similar. The area of HIJK is (2x+9). The area of STUV is (2x-6). The perimeter of HIJK is (x+3). The perimeter of STUV is(x-1). Find the value of x.

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Question 1076669: HIJK and STUV are similar. The area of HIJK is (2x+9). The area of STUV is (2x-6). The perimeter of HIJK is (x+3). The perimeter of STUV is(x-1). Find the value of x.
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
HIJK is the larger figure, and STUV is the smaller figure.

Ratio of their linear measures (for larger to smaller) is .
Ratio of their AREAS IS .

That means, if this ratio is R,






.
.

.
.





-
(arithmetic steps & solution redone)
Answer by ikleyn(52903)   (Show Source): You can put this solution on YOUR website!
.
The equation is 

 = .     (1)


The solution by "josgarithmetic" is .




Plots y = (red) and y = (2x+9)/(2x-6) green) 

To solve (1), cross-multiply and simplify.

You will get the quadratic equation 

 = 0.


It has the solution   =  = 


The only positive solution for x (which works) is  x =  = 9.


Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!

HIJK and STUV are similar. The area of HIJK is (2x+9). The area of STUV is (2x-6). The perimeter of HIJK is (x+3). The perimeter of STUV is(x-1). Find the value of x.


OR





 ----- Cross-multiplying 











(x - 9)(x + 7) = 0

 

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