Trapezoid 15

Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4

Correct answer:

x =  10

Step-by-step explanation:

$$\begin{gathered} A=266 \\ A=(b_1+b_2)h\mathrm{/}2 \\ A=((2x-3)+(2x+1))(x+4)\mathrm{/}2 \\ (2x-3+2x+1)(x+4)\mathrm{/}2=266 \\ 2x^2+7x-270=0 \\ a=2;b=7;c=-270 \\ D=b^2-4ac=7^2-4\cdot 2\cdot (-270)=2209 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{-7\pm \sqrt{2209}}{4}} \\ {x}_{1,2}={\displaystyle \frac{-7\pm 47}{4}} \\ {x}_{1,2}=-1.75\pm 11.75 \\ {x}_1=10 \\ {x}_2=-13.5 \\ \text{ Factored form of the equation: } \\ 2(x-10)(x+13.5)=0 \\ x>0 \\ x=x_1=10=10 \end{gathered}$$

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