Grogg draws triangle ABC. Side BC is 4 inches shorter than side AB. and side AC is 6 inches longer than side BC. The perimeter of the triangle is 31 inches. What is the length of side AB?

AB = 11

Step-by-step explanation:

AB = x

BC = x - 4

AC = 6 + BC    Substitute BC

AC = 6 + (x - 4)

AC = 2 + x

The perimeter of the triangle  is 31

Perimeter =  AB + BC + AC  perimeter is the sum of the sides

 31 = (x )+ (x - 4 ) + (2 + x)

  31 = 3x - 2

   33 = 3x

   11 = x

AB = x = 11 inches

Check:  

AB = x  ;    AB = 11

BC = x - 4;  BC = 11 - 4; BC = 7

AC = 2 + x;  AC = 2 + 11; AC = 13      

  P = 11 + 7 + 13

      = 31

pay attention in your classes and concentrate the best thing you can do to raise your test scores is to pay attention when you're supposed to be learning the material: in class!

take good notes.

do your homework.

use mnemonics and other tricks.

do practice tests.

note: the best i know.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."