Question

problem 10 a painter wants to make a poster that is 4 times larger than this rectangle. what is the area of the scaled copy? 240 inches² 120 inches² 360 inches² 480 inches² 5 inches 3 inches

Explanation:

Step1: Calculate original rectangle area

The area formula for a rectangle is $A = l\times w$. Given $l = 5$ inches and $w = 3$ inches, so $A_{original}=5\times3 = 15$ square - inches.

Step2: Calculate area of scaled - copy

If the new poster is 4 times larger in area than the original rectangle, then $A_{scaled}=4\times A_{original}$. Substitute $A_{original}=15$ into the formula, we get $A_{scaled}=4\times15=60$ square - inches. But if we assume "4 times larger" means the linear dimensions are multiplied by 4. When the linear dimensions of a rectangle are multiplied by a factor $k$, the area is multiplied by $k^{2}$. Here $k = 4$, so $A_{scaled}=k^{2}\times A_{original}$. Since $A_{original}=5\times3 = 15$ square - inches and $k = 4$, then $A_{scaled}=4^{2}\times15=16\times15 = 240$ square - inches.

Answer:

240 inches$^{2}$