A triangle with an perimeter of 23x-7 has two sides with lengths of 5x+7 and 8x-9. What is the length of the third side?

The third side is 10x-5

Step-by-step explanation:

The perimeter of a triangle is given by

P = s1+s2+s3   where s is the side of the triangle

23x-7 = 5x+7  + 8x-9  + s3

Combine like terms

23x-7 = 13x -2  +s3

Subtract 13x from each side

23x -13x-7 = 13x-13x -2  +s3

10x -7 = -2 +s3

Add 2 to each side

10x-7+2 = -2+2 +s3

10x -5 = s3

The third side is 10x-5

x= -3

step-by-step explanation:

step 1: simplify brackets

4 - x - 1 = 6

step 2: simpilfy

3 - x = 6

step 3: subtract 3 from both sides

-x = 6 - 3

step 4: simpilfy 6 - 3

-x = 3

step 5: multiply both sides by -1

x = -3

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2