4. Given a rectangle with dimensions 5 cm and 10 cm, as shown, find the length of the diagonal, if possible.
5 cm
10 cm
help.

Length = 8 cm

width = 6 cm

Step-by-step explanation:

The dimensions of a rectangle are the length and width:

Let x be the length of rectangle, and

y, the width of rectangle

Perimeter equals 2x+2y=28, divide through by 2: x+y=14

Make y the subject, y=14-x, input the value of y into the equation and solve by pythagorean theorem:

x^2 + y^2= 10^2 = 100

x^2 + (14-x)^2 =100

x^2 +196-28x + x^2= 100

2x^2- 28x +196= 100

2x^2 -28x +96 =0

x^2 -14x + 48= 0

(x- 8) (x- 6)= 0

x= 8; or x = 6

The length of rectangle is 8 cm

The width of rectangle is 6 cm

Length = 8 cm

Width = 6 cm

hope that helps

41% of 1 = 0.41
41% of 2 = 0.82
41% of 3 = 1.23
41% of 4 = 1.64
41% of 5 = 2.05
41% of 6 = 2.46
41% of 7 = 2.87
41% of 8 = 3.28
41% of 9 = 3.69
41% of 10 = 4.10
41% of 11 = 4.51
41% of 12 = 4.92
41% of 13 = 5.33
41% of 14 = 5.74
41% of 15 = 6.15
41% of 16 = 6.56
41% of 17 = 6.97
41% of 18 = 7.38
41% of 19 = 7.79
41% of 20 = 8.20
41% of 21 = 8.61
41% of 22 = 9.02
41% of 23 = 9.43
41% of 24 = 9.84
41% of 25 = 10.25
41% of 26 = 10.66
41% of 27 = 11.07
41% of 28 = 11.48
41% of 29 = 11.89
41% of 30 = 12.30
41% of 31 = 12.71
41% of 32 = 13.12
41% of 33 = 13.53
41% of 34 = 13.94
41% of 35 = 14.35
41% of 36 = 14.76
41% of 37 = 15.17
41% of 38 = 15.58
41% of 39 = 15.99
41% of 40 = 16.40
41% of 41 = 16.81
41% of 42 = 17.22
41% of 43 = 17.63
41% of 44 = 18.04
41% of 45 = 18.45
41% of 46 = 18.86
41% of 47 = 19.27
41% of 48 = 19.68
41% of 49 = 20.09
41% of 50 = 20.50
41% of 51 = 20.91
41% of 52 = 21.32
41% of 53 = 21.73
41% of 54 = 22.14
41% of 55 = 22.55
41% of 56 = 22.96
41% of 57 = 23.37
41% of 58 = 23.78
41% of 59 = 24.19
41% of 60 = 24.60
41% of 61 = 25.01
41% of 62 = 25.42
41% of 63 = 25.83
41% of 64 = 26.24
41% of 65 = 26.65
41% of 66 = 27.06
41% of 67 = 27.47
41% of 68 = 27.88
41% of 69 = 28.29
41% of 70 = 28.70
41% of 71 = 29.11
41% of 72 = 29.52
41% of 73 = 29.93
41% of 74 = 30.34
41% of 75 = 30.75
41% of 76 = 31.16
41% of 77 = 31.57
41% of 78 = 31.98
41% of 79 = 32.39
41% of 80 = 32.80
41% of 81 = 33.21
41% of 82 = 33.62
41% of 83 = 34.03
41% of 84 = 34.44
41% of 85 = 34.85
41% of 86 = 35.26
41% of 87 = 35.67
41% of 88 = 36.08
41% of 89 = 36.49
41% of 90 = 36.90
41% of 91 = 37.31
41% of 92 = 37.72
41% of 93 = 38.13
41% of 94 = 38.54
41% of 95 = 38.95
41% of 96 = 39.36
41% of 97 = 39.77
41% of 98 = 40.18
41% of 99 = 40.59
41% of 100 = 41.00