Question

If a 25 in. by 32 in. picture has a wooden frame "x" in. wide surrounding it, which equation can be used to find the total area of the picture and frame?

Answer 1

The frame is at each side of the picture so the area is (25 + 2x) times (32 +2x), (which multiplies out to 4x^2 + 114x + 800 square inches). ie if the frame is an inch and a half wide then the area is 28 x 35 sq ins, ie 980 sq ins.

Answer 2

Answer: The required equation is,

$A = 4x^2+114x+800$

Step-by-step explanation:

Given,

The dimension of the picture is 25 in. by 32 in,

Also, there is a  wooden frame "x" in. wide surrounding it,

So, the dimension of the combined figure of picture and wooden frame would be obtained after adding 2x in the each measure of the picture,

Thus, the dimension of the combined figure is (25+2x) in by (32+2x) in,

The total area of the picture and frame is,

$A=(25+2x)(32+2x)$

$=(25+2x)(32)+(25+2x)(2x)$

$=25(32)+2x(32)+25(2x)+(2x)(2x)$

$=800+64x+50x+4x^2$

$=800+114x+4x^2$

Hence, the equation that can be used to find the total area of the picture and frame would be,

$A=4x^2+114x+800$