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Area of a triangle is given by the formula Upper A equals one half bh A= 1 2 bh. The area of the triangle shown to the right is 120 sq. units. Find its base and height. 3x+9 base x+5 height

Respuesta :

frika

Given:

  • [tex]A=120\ un.^2;[/tex]
  • [tex]\text{height}=x+5\ un.;[/tex]
  • [tex]\text{base}=3x+9\ un.[/tex]

Find: height and base.

Solution: Use given formula for the area:

 [tex]A=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}.[/tex]

Substitute [tex]\text{height}=x+5,[/tex]  [tex]\text{base}=3x+9[/tex] and solve the equation:

[tex]120=\dfrac{1}{2}\cdot (3x+9)\cdot(x+5),\\ \\80=(x+3)(x+5),\\ \\x^2+3x+5x+15-80=0,\\ \\x^2+8x-65=0,\\ \\D=8^2-4\cdot (-65)=64+260=324,\\ \\x_1=\dfrac{-8-18}{2}=-13,\ x_2=\dfrac{-8+18}{2}=5[/tex]

Solution [tex]x_1=-13[/tex] is extra, because then height and base have negative lengths.

When [tex]x_2=5,[/tex]

  • [tex]\text{height}=x+5=5+5=10\ un.;[/tex]
  • [tex]\text{base}=3x+9=3\cdot 5+9=15+9=24\ un.[/tex]

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