Answer:
[tex]\frac{1}{2} (8)(x+4)=3(x+6)\\x=2[/tex]
Step-by-step explanation:
[tex]\frac{1}{2} bh=bh\\\\\frac{1}{2}(8)(x+4)=3(x+6)\\4(x+4)=3x+18\\4x+16=3x+18\\4x=3x+2\\x=2[/tex]
1. set the equation for the area of each shape equal to each other
2. simplify each side until you get [tex]4x+16=3x+18[/tex]
3. subtract 16 from both sides which will give you [tex]4x=3x+2[/tex]
4. subtract 3x from both sides which will give you the value of x. [tex]x=2[/tex]
5. check that [tex]x=2[/tex] is correct by plugging it into the equations
triangle:
[tex]area=\frac{1}{2} (8)(2+4)\\area=4(6)\\area=24[/tex]
rectangle:
[tex]area=3(2+6)\\area=3(8)\\area=24[/tex]
the areas are the same
