# Question 8e319

May 25, 2017

10% was added to the length and width.

#### Explanation:

Let x % is increased in both length and width.

Increased length is $l \cdot \left(1 + 0.01 x\right) = l + 0.01 l x$

Increased width is $w \cdot \left(1 + 0.01 x\right) = w + 0.01 w x$

l*w=300 ; (l+ 0.01lx) * (w+ 0.01wx)=363

$l w + 0.01 x \left(l w + l w\right) + 0.0001 l w {x}^{2} = 363$ or

$300 + 2 \cdot 300 \cdot 0.01 x + 300 \cdot 0.0001 {x}^{2} = 363$ or

$0.03 {x}^{2} + 6 x - 63 = 0 \mathmr{and} 3 {x}^{2} + 600 x - 6300 = 0$ or

${x}^{2} + 200 x - 2100 = 0$

$\left(x + 210\right) \left(x - 10\right) = 0 \therefore x = - 210 \mathmr{and} x = 10$

$x$ cannot be negative so x=10%

10%# was added to the length and width. [Ans]