Question 204754
rectangle's length = L
rectangle's width = W
rectangle's diagonal = D


L = 7 + W
D = 13
use the Phytagoras formula:
{{{D^2 = L^2 + W^2}}}
{{{13^2 = (7 + W)^2 + W^2}}}
{{{169 = 49 + 14W + W^2 + W^2}}}
{{{0 = 49 + 14W + W^2 + W^2 - 169}}}
{{{0 = 2W^2 + 14W + - 120}}}
divide each side by 2
{{{0 = W^2 + 7W + - 60}}}
factorize it:
0 = (W + 12)(W - 5) 
W + 12 = 0 --> W = -12
or
W - 5 = 0 --> W = 5


W = 5 is used because the width of a rectangle must not be a negative value
L = 7 + W = 7 + 5 = 12


so, the length of the rectangle is 12 m