Answer: 5
Step-by-step explanation:
Given
The length of a side is [tex]x+3\ cm[/tex]
The height of a triangle is [tex]2x-5\ cm[/tex]
Area of triangle is [tex]20\ cm^2[/tex]
Area of triangle is given by
[tex]\Rightarrow A=\dfrac{1}{2}\times \text{base}\times \text{height}[/tex]
[tex]\Rightarrow A=\dfrac{1}{2}\times (x+3)\times (2x-5)\\\\\Rightarrow 40=(x+3)\times (2x-5)\\\Rightarrow 2x^2+x-55=0\\\\\Rightarrow x=\dfrac{-1\pm \sqrt{1^2-4(2)(-55)}}{2(2)}\\\\\Rightarrow x=\dfrac{-1\pm 21}{4}\\\\\Rightarrow x=-5.5,5[/tex]
Neglecting negative value
Therefore, the value of x is 5.
