Question

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

Answer 1

Given:

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

Find: height and base.

Solution: Use given formula for the area:

`A=(1)/(2)\cdot \text{base}\cdot \text{height}.`

Substitute
`\text{height}=x+5,`
`\text{base}=3x+9` and solve the equation:

`120=(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=(-8-18)/(2)=-13,\ x_2=(-8+18)/(2)=5`

Solution
`x_1=-13` is extra, because then height and base have negative lengths.

When
`x_2=5,`

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