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:

 $A=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}.$

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

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

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

When $x_2=5,$

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