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What is the area of a rectangle whose length is (5x + 2)cm and whose width is (3x + 1)cm?

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Answer:


\displaystyle A = 15x^2 + 11x + 2\text{ cm}^2

Explanation:

We are given that the length and width of a rectangle is given by:


\ell = (5x + 2)\text{ cm} \text{ and } w = (3x+1)\text{ cm}

And we want to find the area of the rectangle.

Recall that the area of a rectangle is given by:


\displaystyle A = w\ell

Substitute:


A = (3x+1)(5x+2)

Expand and simplify:


\displaystyle \begin{aligned}A &= 5x(3x+1) + 2(3x+1) \\ &= (15x^2+5x)+(6x+2) \\ &= (15x^2)+(5x+6x)+(2) \\ &= 15x^2 + 11x +2 \end{aligned}

Hence, the area of the rectangle is:


\displaystyle A = 15x^2 + 11x + 2\text{ cm}^2

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