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Given that a rectangle with length 3x inches and width x + 5 inches has the property that its area and perimeter have equal values, what is X?

 Oct 20, 2019
 #1
avatar+198 
+1

Area = 3X(X + 5) = 3X^2 + 15X

Perimeter = 2(3X) + 2(X + 5) = 6X + 2X + 10 = 8X + 10

 

 

3X^2 + 15X = 8X + 10

3X^2 + 7X - 10 = 0

3X^2  - 3X + 10X - 10 = 0

3X(X-1)+10(X-1) = 0

(3X + 10)(X -1) = 0

X = 1, X = -10/3

 

We only consider the positive solution in this case. X = 1

 Oct 20, 2019
 #2
avatar+2390 
0

Good job Mathlete!

CalculatorUser  Oct 20, 2019

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