a - length of side of a square
t - length of side of a triangle
The perimeter of a square:
The perimeter of a triangle:
We have the area of a triangle:
The formula of an area of an equilateral trinagle:
Substitute:
<em>multiply both sides by 4</em>
<em>divide both sides by
</em>
The perimeter of a triangle:
Substitute to the formula of a perimeter of a square:
<em>divide both sides by 4</em>
The formula of a diagonal of a square:
Substitute:
Answer: The two roots are x = 3/2 and x = -2
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Explanation:
You have the right idea so far. But the two numbers should be 3 and -4 since
The -1 being the coefficient of the x term.
This means you need to change the -3x and 4x to 3x and -4x respectively. The other inner boxes are correct.
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Refer to the diagram below to see one way to fill out the box method, and that helps determine the factorization.
If we place a 2x to the left of -2x^2, then we need an -x up top because 2x*(-x) = -2x^2
Then based on that outer 2x, we need a -2 up top over the -4x. That way we get 2x*(-2) = -4x
So we have the factor -x-2 along the top
The last thing missing is the -3 to the left of 3x. Note how -3*(-x) = 3x in the left corner and -3*(-2) = 6 in the lower right corner.
We have the factor 2x-3 along the left side.
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The two factors are (2x-3) and (-x-2) which leads to the factorization (x+3)(-x+2)
The last thing to do is set each factor equal to 0 and solve for x
The two roots are x = 3/2 and x = -2
