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The height of a triangle is 1.95 centimeters less than 2.5 times the corresponding base. The area of the triangle is 112.8 square centimeters. The quadratic equation that correctly models this situation is 2.5x^2−1.95x=225.6 or 2.5x^2−1.95x−225.6=0, where x represents the base of the triangle. How long is the base of this triangle?

Respuesta :

debmommabear

Answer:

9.89 cm.

Step-by-step explanation:

Let's solve your equation step-by-step.

2.5x2−1.95x−225.6=0

Step 1: Use quadratic formula with a=2.5, b=-1.95, c=-225.6.

x=

−b±√b2−4ac

2a

x=

−(−1.95)±√(−1.95)2−4(2.5)(−225.6)

2(2.5)

x=

1.95±√2259.8025

5

x=9.89747600575463,−9.117476005754629

Answer:

9.897 cm ( approx )

Step-by-step explanation:

Given equation is,

[tex]2.5x^2-1.95x-225.6=0[/tex]

Where,

x = base of the triangle, ( in cm )

By further simplifying the above equation,

[tex]250x^2 - 195x - 22560 =0[/tex]

[tex]50x^2 - 39x - 4512=0[/tex]

By quadratic formula,

[tex]x=\frac{-(-39)\pm \sqrt{(-39)^2-4\times 50\times -4512}}{2\times 50}[/tex]

[tex]x=\frac{39\pm \sqrt{1521+902400}}{100}[/tex]

[tex]x=\frac{39\pm \sqrt{903921}}{100}[/tex]

[tex]\implies x = 9.897\text{ or }x=-9.117[/tex]

Since, side can not be negative,

Hence, the length of the base = 9.897 cm.

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