Answer:
15 cm , 20 cm
Step-by-step explanation:
Framing algebraic equation and solving to find the unknown value:
Let the length of the ticket be 'x' cm and width be 'y' cm.
Perimeter of the rectangle = 2* (length + width)
2 * (x + y) = 70
Divide the entire equation by 2,
[tex]\sf \dfrac{2*(x +y) }{2}= \dfrac{70}{2}[/tex]
x + y = 35
x= 35 - y
Area of the rectangle ticket = length *width.
It is given that the area is 300 cm².
⇒ x * y = 300
Substitute x = 35 - y in the above equation,
(35 -y)*y = 300
Use Distributive property,
35y - y² = 70
0 = y² -35y + 300
y² - 35y + 300 = 0
sum = -35
Product = 300
Factors are: (-15), (-20)
{-15* -20 = 300 and (-15) + (-20) = -35}
Rewrite the middle term using the factors,
y² - 15y - 20y + 300 = 0
y* (y - 15) - 20*(y - 15) = 0
(y -15) (y -20) = 0
y - 15 = 0 ; y - 20 = 0
y = 15 ; y = 20
Dimensions of the ticket are 15 cm , 20 cm