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.
a. gerard wrote the equation b/3 = 3 1/2. explain what bb represents in the equation.
b. determine the area of triangle b.

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:

We add these fractions:

The equation with this part solved is:

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

And then, we can solve the rest by inverting the second fraction () and multiplying it by the first one:

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

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb