Question 1168781
the area of the table top is 10 square meters.
the length of the table is 3 meters longer than the width.


let x = the length
let y = the width.
the area of the table top is equal to x * y


since the length of the table top is 3 meters longer than the width, you get:
x = 3y


area = x * y becomes area = 3y * y, after you replace x with 3y.


simplify to get:
area = 3y^2


since the area is 10 square meters,  you get:
10 = 3y^2


divide both sides of this equation by 3 to get:
10/3 = y^2


solve for y to get:
y = plus or minus sqrt(10/3)


since y can't be negative, y must be equal to sqrt(10/3)
since x = 3y, then x must be equal to 3 * sqrt(10/3)


the area of the table is equal to x * y.
x * y = 3 * sqrt(10/3) * sqrt(10/3)
since sqrt(10/3) * sqrt(10/3) = 10/3, the area of the table becomes:
area = 3 * 10/3
simplify to get:
area = 10


this confirms the solution is correct.
the solution is:


length = 3 * sqrt(10/3)
width = sqrt(10/3)



in decimal format, .....


length = 5.477225575 meters.
width = 1.825741858 meters.