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

1     sepan

2     encuentren

3     tenga

4     hable

5   parezca

6   llegue

so, converting firstly the mixed fractions to improper fractions and then "adding".