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This is Algebra 1 Please HELP

This is Algebra 1 Please HELP-example-1

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We know that the area of a rectangle is length * width, and the area of a triangle is 1/2 * base * height. However, we know that the areas are equal, or that

lw = 1/2bh

If we substitute in the measurements that we know, we can solve the following equation for x.

5x + 1 (x) = 1/2(8x)(x+1)

Let's simplify this equation by multiplying.

5x² + x = 4x² + 4x

Now, let's bring all of the variables to one side of the equation.

x² - 3x = 0

Finally, we should factor out the Greatest Common Factor.

x(x-3) = 0

Therefore, by the Zero Product Property, x = 0, 3. But since the measurement of the short side length of the rectangle is x, it cannot be zero. Thus, x = 3.

The question asks for the area of the rectangle, which is 5x² + x.

Let's solve this expression for x = 3.

5(3)² + 3
5(9) + 3
45 + 3
48

Therefore, the area of the rectangle is 48 square units, or option B.
User Franky
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