SOLUTION: The perimeter of a rectangle is 30 cm. The area is 36 cm^2. Find the longest dimension of the rectangle.

Question 926741: The perimeter of a rectangle is 30 cm. The area is 36 cm^2. Find the longest dimension of the rectangle.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
2L + 2w = 30
Lw = 36
L = 36/w
---
2L + 2w = 30
2(36/w) + 2w = 30
72/w + 2w - 30 = 0
w(72/w + 2w - 30 = 0)
72 + 2ww - 30w = 0
2ww - 30w + 72 = 0
---
the above quadratic equation is in standard form, with a=2, b=-30 and c=72
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
2 -30 72
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic has two real roots at:
---
w = 3
w = 12
---
use the root w = 3 (using either root works fine for this problem):
L = 36/w
L = 36/3
L = 12
---
answer:
the longest dimension of the rectangle = 12 cm
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
RELATED QUESTIONS
the perimeter of a rectangle is 60 cm and its area is 216 sq cm. Find its... (answered by solver91311)

the perimeter of a rectangle in 30 cm and its area is 50 cm squared. find in centre... (answered by mananth)

THE LENGTH OF A RECTANGLE IS 12 CM GREATER THAN ITS WIDTH. IF THE PERIMETER OF THE... (answered by josgarithmetic)

the perimeter of a rectangle is 50 cm and its area is 144 square centimeters.Find the... (answered by josgarithmetic)

find the area of its region if the perimeter of a rectangle is 36... (answered by Theo)

the length of a rectangle is thrice width. if the length is increase by 8 cm and width is (answered by mohanraj04)

Find the dimension and the maximum area of a rectangle if its perimeter is... (answered by srinivas.g)

the length of a rectangle plus its width is 30 cm. the area is 221 square cm. how long is (answered by sarah_adam)

The perimeter of a rectangle is 40 cm. Four times the length is 3 cm more than 7 times... (answered by fractalier)