Problema Solution
mang jose wants to make a table which has an area of 6m2 the length of the table has to be 1 meter longer than the width
a.if the width of the table is pmeters what willbe its length?
b.form a quadratic equation that represents the situation?
c.determine whether the dimensions of the table are ratinal numbers?
d.give the dimensions of the table?
Answer provided by our tutors
let
l = the length of the table
w = the width of the table
A = 6 m^2 the area of the table
the length of the table has to be 1 meter longer than the width
l = w + 1
a.if the width of the table is p meters what will be its length?
l = p + 1
b.form a quadratic equation that represents the situation?
A = l*w
l*w = 6
plug w = p and l = p + 1 into the last equation
(p + 1)*p = 6
p^2 + p - 6 = 0
c.determine whether the dimensions of the table are rational numbers?
the dimensions of the table are rational numbers if the solution of the quadratic equation p^2 + p - 6 = 0 is a rational number
if square root of b^2 - 4ac is a rational where a = 1, b = 1, c = -6 then the quadratic equation has rational solutions
1^2 - 4*(-6)*1 = 1 + 24 = 25
square root of 25 is 5 thus the dimensions of the table are rational numbers
d.give the dimensions of the table?
p^2 + p - 6 = 0
by solving we find and consider the positive roots since the dimensions of the table must be positive numbers
p = 2
click here to see the step by step solution of the equation
l = 2 + 1
l = 3 m
w = 2 m
the length of the table is 3 meters.
the width of the table is 2 meters.