Question

if the green rectangle had the area of 1x and the blue square had an area of $x^{2}$ what is the area of this new rectangle?
$x^{2}+2x$
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your classmates said:
mauricio alvarado bermudez
$x + x^{2}$
briceida hernandez ornelaz
$x^{2}+2x$
supiesi takeifanga
$x^{2}+2x$

Explanation:

Step1: Analyze the components

The new rectangle is composed of the blue square (area \(x^{2}\)) and two green rectangles (each with area \(x\)).

Step2: Calculate the total area

The total area is the sum of the areas of its components. So we add the area of the blue square and the two green rectangles. Using the formula for the sum of areas \(A = x^{2}+x + x\).
Simplifying \(x + x=2x\), so \(A=x^{2}+2x\).

Answer:

\(x^{2}+2x\)