An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 9 more than three times the length of the bottom of the triangle. The last side is 7 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.

perimeter:6x+15

EXPLANATION

The perimeter of the triangle is the distance around the triangle.

We need to apply our ability to convert word problems in to mathematical expressions.

we were told that the bottom of the triangle is  units.

From the diagram perimeter

Four times the length of the bottom will be .

12 more than 4 times the bottom will be  

Hence another side of the triangle is

Finally we were told that the last side is 3 more than the bottom, that will be

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.