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A(x)=(2x+8)(2x+10)
The function models
A, the area, in square inches, of a rectangular framed picture with an 8 inch by 10 inch picture and a frame width of
x inches. What is the area, in square inches, of the framed picture if the frame is 0.5 inch wide?

$A(x)=(2 x+8)(2 x+10)$ $\newline$ The function models $A$ , the area, in square inches, of a rectangular framed picture with an $8$ inch by $10$ inch picture and a frame width of $x$ inches. What is the area, in square inches, of the framed picture if the frame is $0$ . $5$ inch wide?

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Scale drawings: word problems

Full solution

Q.

A(x)=(2 x+8)(2 x+10)

\newline

The function models

A

, the area, in square inches, of a rectangular framed picture with an

8

inch by

10

inch picture and a frame width of

x

inches. What is the area, in square inches, of the framed picture if the frame is

0

.

5

inch wide?

Identify function and value: Identify the given function and the value of $x$ to be substituted. $\newline$ The function $A(x) = (2x + 8)(2x + 10)$ represents the area of the framed picture. We are given that the frame width is $x = 0.5$ inches.
Substitute value and find area: Substitute the value of $x$ into the function to find the area. $A(0.5) = (2(0.5) + 8)(2(0.5) + 10) = (1 + 8)(1 + 10)$
Perform arithmetic operations: Perform the arithmetic operations to calculate the area. $\newline$ $A(0.5) = (9)(11) = 99$ square inches

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