Answers:
A. B 1/3 represents the area of triangle B
B. Triangle B area = 21/2 m² or 10 1/2 m² or 10.5 m²
Step-by-step explanation:
Ok, we have two triangles measured in square meters (m²)
∆ a = 1/3 b and ∆ b = 3 1/2
Since these two areas have something in common (symbol a) we can consider they are almost the same, so we put them like this:
∆ a => 1/3 b = 3 1/2 <= ∆ b
Now that we know we can move some values. first we are gonna multiply the mixed fraction (3 1/2) to make it a regular fraction. As 3 is a whole, we can also write it on the following way:
[tex]\frac{3}{1} +\frac{1}{2}[/tex]
We add these fractions:
[tex]\frac{3}{1} +\frac{1}{2} = \frac{(3x2)+(1x1)}{1x2} =\frac{6+1}{2} =\frac{7}{2}[/tex]
The equation with this part solved is:
[tex]\frac{1}{3} b=\frac{7}{2}[/tex]
Since the 1/3 is multiplying, it goes to the other side dividing the number on the right:
[tex]b=(\frac{7}{2} )/(\frac{1}{3} )[/tex]
And then, we can solve the rest by inverting the second fraction ([tex]\frac{1}{3}[/tex]) and multiplying it by the first one:
[tex]b=\frac{7}{2} / \frac{1}{3} \\[/tex]
[tex]b=\frac{7}{2} x \frac{3}{1} =\frac{7x3}{2x1} =\frac{21}{2}[/tex]
And that's it. Let me know if you have any doubts :D
