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Algebra
Pregunta

A framed picture has a total area \( y \) , in squ...

A framed picture has a total area \( y \) , in square inches. The thickness of the frame is represented by \( x \) , in inches. The equation \( y = ( 8 + 2 x ) ( 10 + 2 x ) \) relates these two variables. 

1. What are the length and width of the picture without the frame? 

2. What would a solution to the equation \( 100 = ( 8 + 2 x ) ( 10 + 2 x ) \) mean in this situation? 

Answer

length=(8+2x) inches

width=(10+2x) inches

\(100= \left(8+ 2x\right)\left(10+ 2x\right)\quad : \quad x= \frac{- 9+ \sqrt{101}}{2},\space x= -\frac{9+ \sqrt{101}}{2}\)

2x+8=-1+\(\sqrt{101}\)

2x+10=1+\(\sqrt{101}\)

Solución
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