Respuesta :
Answer:
1.5 inches.
Step-by-step explanation:
A picture measuring 4 inches by 6 inches is placed inside a frame which has equal width around the entire picture.
The area of the frame and the picture is 63 square inches.
Question asked:
What is the width of the frame ?
Solution:
Let width of the frame = [tex]x[/tex]
Then combined length (frame and picture) = [tex]6+x+x=6+2x\ inches[/tex]
Similarly, combined width (frame and picture) = [tex]4+x+x=4+2x \ inches[/tex]
By using:-[tex]Area\ of\ rectangle=length\times width[/tex]
Combined area of the frame and the picture = 63 square inches
-[tex]length\times width=63\\(6+2x)(4+2x)=63\\\\6(4+2x)+2x(4+2x)=63\\24+12x+8x+4x^{2} =63\\24+20x+4x^{2} =63[/tex]
Subtracting both sides by 24
[tex]4x^{2} +20x= 39[/tex]
Subtracting both sides by 39
[tex]4x^{2} +20x-39= 39-39\\4x^{2} +20x-39=0[/tex]
[tex]4x^{2} + 26x - 6x-39 = 0\\Taking\ common\\[/tex]
[tex]2x(2x+13)-3 (2x+13)=0\\2x+13=0,2x-3=0\\2x=0-13,2x= 0+3[/tex]
[tex]x=\frac{-13}{2} ,x=\frac{3}{2}[/tex]
Since, width can never be in negative thus, [tex]x=\frac{3}{2} = 1.5 \ inches[/tex]
Therefore, width of the frame is 1.5 inches around the entire picture.
