Respuesta :
Answer:
The correct answer is A. 1.5w² + 5w + 4
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Height of the portrait = 1.5 times its width in inches
Frame = 2 inches all along its perimeter
2. What is an expression for the area of the framed portrait in terms of w?
Let's recall that the area of a rectangle is length or height * width.
A = height * width
Now, we can replace in terms of w:
A = 1.5w * w
But we need to add the 2 inches of the frame, this way:
A = (1.5w + 2) * (w + 2)
A = 1.5w² + 2w + 3w + 4
A = 1.5w² + 5w + 4
The correct answer is A. 1.5w² + 5w + 4
The area of the framed portrait in terms of w is [tex]\rm 1.5w^2 + 5w+ 4[/tex].
Given that,
A portrait without its frame has a height 1.5 times its width w, in inches.
Its frame is 2 in. wide all along its perimeter.
We have to determine,
What is an expression for the area of the framed portrait in terms of w?
According to the question,
The height of the portrait is 1.5w and its width w,
And its frame is 2 in. wide all along its perimeter.
The new height becomes( 1.5w +2) and width (w+2).
The area of the framed portrait in terms of w is determined by using the formula,
[tex]\rm Area = Height \times width[/tex]
Substitute all values in the formula
[tex]\rm Area = (1.5w+2)\times (w+2)\\\\Area = 1.5w(w+2) +2(w+2)\\\\Area = 1.5w^2+3w+2w+4\\\\Area = 1.5w^2+5w +4[/tex]
Hence, The area of the framed portrait in terms of w is [tex]\rm 1.5w^2 + 5w+ 4[/tex].
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