5. Rewriting Equations and Formulas
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Divide the figure into a right triangle and a rectangle.
Example Solution: h=6
Let's take a look at the figure. We need to give a possible value for h.
First, we will divide the figure into a right triangle and a rectangle, labeling the base of the triangle a. Since the base of the figure is 8 cm and the base of the triangle is a, the length of the rectangle is the difference between those two values, 8-a.
Recall that area of a rectangle is its length multiplied by its width. In our case, the length and width are h and 8-a, respectively. Let's substitute those into the formula. A_R=l w ⇔ A_R = h( 8-a) We found that h(8-a) represents the area of the rectangle.
Area of a triangle is half the product of its base and height. In the diagram we see that a is the base of the triangle, and h is its corresponding height. We can substitute those values into the formula. A_T=1/2bh ⇔ A_T = 1/2 a h
.LHS /h.=.RHS /h.
LHS-8=RHS-8
LHS * (-1)=RHS* (-1)
LHS * 2=RHS* 2
Commutative Property of Addition
Rearrange equation
Looking at the figure, we can tell that h should probably be less 8. Therefore, let's try a few values that are less than 8 but larger than 0. We can use a calculator for that.
| h | 16- 80/h | a |
|---|---|---|
| 4 | 16- 80/4 | - 4 |
| 5 | 16- 80/5 | 0 |
| 6 | 16- 80/6 | 2.7 |
| 7 | 16- 80/7 | 4.57 |
We see that only one of the possible values of h we tested
is a viable result. This gives us the following figure.
