a If the base of the first triangle is x and the length of the two equal sides is y, we can write an equation to calculate the perimeter P of the triangle.
x+2y=P
Let's look at the given graph.
We can use the equation given on the graph y= 6- 12x to solve for P.
The perimeter of the first triangle is 12 meters. We are told that the perimeter of the second rectangle is 8 meters more than the perimeter of the first triangle. Let's calculate the perimeter of the second triangle!
12+8=20 meters
We can now write an equation that describes the perimeter for the second triangle.
x+2y=20
Let's rewrite this equation into slope-intercept form so that we may graph it.
Let's graph this equation! Notice that the endpoints are left open, as neither the width nor the length can be equal to the full perimeter. This would mean that the other sides have a length of 0, which is not possible.
b Let's graph both of the lines on the same coordinate plane and compare.
Comparing the graphs, we can see that the slopes are the same. We can also see that the green graph's endpoints are farther from the origin.
