Math  /  Geometry

Question9. If GFEGHJ\triangle G F E \sim \triangle G H J, find the value of xx.

Studdy Solution
Solve the quadratic equation 2x2+13x84=0 2x^2 + 13x - 84 = 0 using the quadratic formula:
x=b±b24ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
where a=2 a = 2 , b=13 b = 13 , and c=84 c = -84 .
Calculate the discriminant:
b24ac=1324×2×(84)b^2 - 4ac = 13^2 - 4 \times 2 \times (-84) =169+672= 169 + 672 =841= 841
Calculate x x :
x=13±8414x = \frac{-13 \pm \sqrt{841}}{4} x=13±294x = \frac{-13 \pm 29}{4}
Calculate the two possible solutions:
x1=13+294=164=4x_1 = \frac{-13 + 29}{4} = \frac{16}{4} = 4 x2=13294=424=10.5x_2 = \frac{-13 - 29}{4} = \frac{-42}{4} = -10.5
Since x x represents a length, it must be positive. Therefore, x=4 x = 4 .
The value of x x is:
4 \boxed{4}

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