Question

One side of a rectangle is 7 more than the other. If you increase the smaller side by 2, and double the longer side, find the area of the new rectangle.

Answer 1

Answer:

4x + 28 + 2x + 4

Step-by-step explanation:

old rectangle = 4x + 14

new rectangle = 4x + (14+x)2 + (2)2

new rectangle = 4x + 28+2x + 4

Answer 2

The expression that represents the area of the new rectangle after its smaller side is increased by 2 and the longer side is double is: $\mathbf{x^3 + 16x^2 + 77x + 98}$

Recall:

Area of a rectangle = length x width

Given:

Let a side of the rectangle = x (smaller side)

One other side of the rectangle = x + 7 (longer side)

Thus,

Increasing the smaller side by 2, we have:

• x + 2

Doubling the longer side, we would have:

• $(x + 7)^2$

Area of the new rectangle would be:

= $(x + 2) \times (x + 7)^2$

• Solve

$(x + 2) \times (x^2 + 14x + 49)\\\\x(x^2 + 14x + 49) + 2(x^2 + 14x + 49)\\\\x^3 + 14x^2 + 49 x + 2x^2 + 28x + 98$

• Add like terms

$\mathbf{x^3 + 16x^2 + 77x + 98}$

In conclusion, the expression that represents the area of the new rectangle after its smaller side is increased by 2 and the longer side is double is: $\mathbf{x^3 + 16x^2 + 77x + 98}$

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