Question

Triangle A has an area equal to one-third the area of Triangle B. Triangle A has an area of 3 1/2 square meters.

Answer 1

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:

$\frac{3}{1} +\frac{1}{2}$

We add these fractions:

$\frac{3}{1} +\frac{1}{2} = \frac{(3x2)+(1x1)}{1x2} =\frac{6+1}{2} =\frac{7}{2}$

The equation with this part solved is:

$\frac{1}{3} b=\frac{7}{2}$

Since the 1/3 is multiplying, it goes to the other side dividing the number on the right:

$b=(\frac{7}{2} )/(\frac{1}{3} )$

And then, we can solve the rest by inverting the second fraction ($\frac{1}{3}$) and multiplying it by the first one:

$b=\frac{7}{2} / \frac{1}{3}$

$b=\frac{7}{2} x \frac{3}{1} =\frac{7x3}{2x1} =\frac{21}{2}$

And that's it. Let me know if you have any doubts :D