# Originally the dimensions of a rectangle were 20cm by 23cm. When both dimensions were decreased by the same amount, the area of the rectangle decreased by 120cm². How do you find the dimensions of the new rectangle?

The new dimensions are:

$a = 17$
$b = 20$

#### Explanation:

Original area:
${S}_{1} = 20 \times 23 = 460 c {m}^{2}$

New area:
${S}_{2} = 460 - 120 = 340 c {m}^{2}$

$\left(20 - x\right) \times \left(23 - x\right) = 340$

$460 - 20 x - 23 x + {x}^{2} = 340$

${x}^{2} - 43 x + 120 = 0$

${x}_{1} = 40$ (discharged because is higher than 20 and 23)

${x}_{2} = 3$

The new dimensions are:

$a = 20 - 3 = 17$
$b = 23 - 3 = 20$