Question 1092306
<br>Let x and y be the length and width of the room.<br>
The perimeter is 80:
{{{2x+2y = 80}}}
{{{x+y = 40}}}  (1)<br>
The diagonal of the room is the square root of 1312:
{{{sqrt(x^2+y^2) = sqrt(1312)}}}
{{{x^2+y^2 = 1312}}}  (2)<br>
To solve the system of equations (1) and (2), first square (1):
{{{x^2 + 2xy + y^2 = 1600}}}  (3)<br>
Then subtract (2) from (3):
{{{2xy = 288}}}
{{{xy = 144}}}  (4)<br>
You could solve (1) and (4) algebraically; but it's faster just to look for a pair of numbers whose sum is 40 and whose product is 144.  Those numbers are 36 and 4.<br>
Liboko has a very long and narrow storeroom with length 36m and width 4m.