We want to find x knowing that the two figures below have equal areas.
Let's recall the formulas for the area of a square and the area of a rectangle.
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Area of a Square:& & Area of a Rectangle:
A = s^2 & & A = l wWe can use these formulas to write expressions for the areas of the figures from the given diagram.
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Area of Given Square:& & Area of Given Rectangle:
A = ( 2x)^2 && A = ( x+10)( 2x-3)
Let's equate these expressions and solve the resulting equation for x.
The resulting equation is quadratic equation, so let's use the quadratic formula to solve it.
ax^2+ bx+ c=0 ⇕ x=- b± sqrt(b^2-4 a c)/2 a
Now let's the values of a, b, and c for our equation.
-2x^2+17x-30 = 0 ⇕ -2x^2+ 17x+( - 30)=0
We see that a= -2, b= 17, and c= - 30. Let's substitute these values into the quadratic formula.
