Question

A rectangle has an area of 21.42 cm2. When both the length and width of the rectangle are increased by 1.50 cm, the area of the rectangle becomes 38.22 cm2. Calculate the length of the longer of the two sides of the initial rectangle.

Answer 1

would you agree that length times width is area?

Answer 2

l w = k
(l+n) (w+n) = c

let, say l=k/w and sub in

(k/w+n) (w+n) = c

multiplying by w we get

(k+wn) (w+n) = wc which is just a quadratic in w to determine

Answer 3

kw + kn + nw^2 + n^2 w = wc

n w^2 + (n^2 + k - c) w + kn = 0

for the given values of n,k,c from the problem

Answer 4

the 2 values you get for w, will actually define the 2 required sides, pick the larger for the solution

Answer 5

what does k stand for?

Answer 6

the area of a rectangle, before adding something to the sides ...

lw = k is simpler to work with instead of writing in all the numbers to get in the way

Answer 7

im still kinda confused, do you think you could explain it some more?

Answer 8

is c the area after adding? what is n?

Answer 9

c is the area after adding, n is what they added yes

Answer 10

\[(1.5) w^2 + ((1.5)^2 + (21.42) - (38.22)) w + (21.42)(1.5) = 0\]
still messy, might have been better to get teh quadratic formula first then inserted values :)

Answer 11

\[\underbrace{n}_a~ w^2 +\underbrace{ (n^2 + k - c)}_b~ w + \underbrace{kn}_c = 0\]
\[w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
still a mess but at least we dont have to fight the numbers till the end

Answer 12

or using the other one, and wolfs brains :)

http://www.wolframalpha.com/input/?i=%281.5%29+w%5E2+%2B+%28%281.5%29%5E2+%2B+%2821.42%29+-+%2838.22%29%29+w+%2B+%2821.42%29%281.5%29+%3D+0

Answer 13

6.3 * 3.4 = 21.42

and

(6.3+1.5) * (3.4+1.5) = 38.22

as required

Answer 14

thank you!

Answer 15

who ever assigned this to you .. you need to slap upside the head :) but at least you tried to participate and i hope my method proved insightful at least.