Question

What is the value of x if the length and the breadth of a rectangle are (3x +1)cm and( 2x -1)cm respectively and whose area is 144cm² ?

Answer 1

(3x + 1) (2x - 1) = 144

6 x^2 - x - 145 = 0

use quadratic formula to find x

Answer 2

L = length

B = breadth

A = Area

A = L ∙ B

( 3 x + 1 ) ∙ ( 2 x - 1 ) = 144

6 x² + 2 x - 3 x - 1 = 144

6 x² x - 1 = 144

Subtract 144 to both sides

6 x² - x - 145 = 0

The solutions are:

x = - 29 / 6 and x = 5

Length and breadth cannot be negative so x = 5 cm

By the way:

L = ( 3 x + 1 ) = 3 ∙ 5 + 1 = 15 + 1 = 16 cm

B = ( 2 x - 1 ) = 2 ∙ 5 - 1 = 10 - 1 = 9 cm

A = 16 cm ∙ 9 cm = 144cm²