HELP

Here's 15

Call the first angle x

The second = 2x + 10

The third = 5[2x + 10] - 10    and we have

x + 2x + 10 + 5[2x + 10] - 10  = 180    simplify

x + 2x + 10 + 10x + 50 - 10   = 180

13x + 50  = 180     subtract 50 from both sides

13x  =  130    divide both sides by 13    and x  = 10    and this is the first angle

2(10) + 10   = 30    and this is the second

5[30] - 10   = 140    and this is the third

Here's 2

Call the first side, x

The second side  is  x+ 3

The third side is 3(x + 3)  - 2

And we have

x + [x + 3}  + 3(x + 3)  - 2  = 45     simplify

x + x + 3 + 3x + 9  - 2  = 45

5x + 10   = 45     subtract 10 from both sides

5x = 35     divide both sides by 5

x = 7   cm

And the third side = 3(7 + 3) - 2  = 3(10)  - 2   =  28 cm

Here's 4

L = 3W + 2

And the prerimeter  =  2[L + W]  = 2[ (2W + 2) + W ]    and we have

2 [ (3W + 2) + W ]  = 36   simplify

2 [ 4W + 2 ]   = 36       divide both sides by 2

4W + 2  = 18       subtract  2 from both sides

4W  = 16         divide both sides by  4

W = 4 cm

L= 3(4)) + 2   =  12 + 2   = 14  cm

Here's 8

L = W + 3

So

2 [ L + W ]   = perimeter

2 [ (W + 3) + W  ]  = 30   simplify....divide both sides by 2

2W + 3  = 15        subtract 3 from both sides

2W   =  12     so W = 6  and L = W + 3 = 9

And area  = L * W    =     9 * 6   = 54  cm^2

Here's 10

2L  + 2W = 20      divide both sides by 2

W + L   = 10    →  W = 10 - L     .....the original area   =  W*L  = [10 - L]L   =  10L - L^2

And we have that

[L + 2 ] * [ W + 3}  = 10L - L^2 + 30

[L + 2] * [ 10 - L + 3]   = 10L - L^2 + 30   simplify

[ L + 2] * [ 13 - L]  = 10L - L^2 + 30

-L^2 + 26 + 13L -2L   = 10L - L^2 + 30

26 + 11L  = 10L + 30       subtract  26 , 10L from both sides

L  = 4 m       and   W  = 10 - L   =  6 m      and these are the original dimensions

Here's 12

The original area = s^2

So

[s + 2] [s + 2 ]  = s^2 + 28   simplify

s^2 + 4s + 4  = s^2 + 28     subtract s^2 from both sides

4s + 4  = 28      subtract 4 from both sides

4s  = 24    divide both sides by  4

s = 6 cm    this is the side of the original square....and the original perimeter was 4 times this = 24 cm

Here's 14

Call the smallest angle, x

The second = 2x

The third = 3x

And we have

x + 2x + 3x  = 180

6x = 180     divide both sides by 6

x = 30

2x = 60

3x = 90

Here's 6

L = 3W     original  area =  L * W   =  3W*W =   3W^2

[W - 1] [ L + 3] = 3W^2 + 72

[ W - 1] [ 3W + 3]  = 3W^2 + 72

3W^2  - 3W + 3W - 3   = 3W^2 + 72    

3W^2  - 3  = 3W^2 + 72         and this has no answer......(????)