Question #8e319

Question

1585 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-25T11:30:37

$10 %$ $10%$ was added to the length and width.

Let $x %$ $x %$ is increased in both length and width.

Increased length is $l \cdot (1 + 0.01 x) = l + 0.01 l x$ $l*(1+0.01x)= l+ 0.01lx$

Increased width is $w \cdot (1 + 0.01 x) = w + 0.01 w x$ $w*(1+0.01x)= w+ 0.01wx$

$l \cdot w = 300; (l + 0.01 l x) \cdot (w + 0.01 w x) = 363$ $l*w=300 ; (l+ 0.01lx) * (w+ 0.01wx)=363$

$l w + 0.01 x (l w + l w) + 0.0001 l w x^{2} = 363$ $lw+0.01x(lw+lw)+0.0001lwx^2=363$ or

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

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

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

$(x+210)(x-10)=0 :. x=-210 or x=10$

$x$ cannot be negative so $x=10%$

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