The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?
2006-08-25 12:17:10 · 9 answers · asked by superhomer1221 2 in Science & Mathematics ➔ Mathematics
The diagonal of a rectangle relates to the sides:
(diagonal)^2 = (length)^2 + (width)^2
They tell you width + 1 = length
Say its: W + 1 = L
and diagonal = 4 cm
Plug these into the equation
(4)^2 = (W + 1)^2 + W^2
16 = (W^2 + 2W + 1) + W^2
16 = 2W^2 + 2W + 1
2W^2 + 2W - 15 = 0
Quadratic formula:
W = [-2 +/- sqrt( (2^2) - (4)(-15)(2) ) ] / 2(2)
W = [-2 +/- sqrt( 4 + 120 ) ] / 4
W = [-2 +/- sqrt(124) ] / 4
W = [-2 +/- 2*sqrt(31) ] / 4
Since width can only be positive,
W = [sqrt(31) - 1] / 2 cm
L = 1 + [sqrt(31) - 1] / 2 cm
2006-08-25 15:28:44 · answer #1 · answered by Anonymous · 0⤊ 0⤋
There is no such thing as dumb guys, just smarter gals.
The diagonal of a rectangle and the width and the length all make a right triangle, so you can use pythagorean theorum to figure it...
x^2 + (X+1)^2 = 16
2006-08-25 19:28:55 · answer #2 · answered by just browsin 6 · 0⤊ 0⤋
OK....lets see.....
let L be the length .....
and W be the width....
then you have
L = W + 1
then the pythgorean thm
(W+1)^2 + W^2 = 16
W^2 + 2 W + 1 + W^2 = 16
2w^2 + 2W -15 = 0
let homer to figure it out
2006-08-25 19:29:51 · answer #3 · answered by David F 2 · 0⤊ 0⤋
l = w+1
w^2 + (w+1)^2 = 16
w^2 + w^2 + 2w + 1 - 16 = 0
2w^2 + 2w -15 =0
This doesn't factor so you need to use the Quadratic formula for the answer
2006-08-25 21:19:05 · answer #4 · answered by MollyMAM 6 · 0⤊ 0⤋
Use the pathagorean theorem to sole an issolese triangle....a and b are the legs and c is the hypoteneuse.
a^2+b^2=c^2
a^2+b^2=4^2
a^2+b^2=16
Now solve the problem.
2006-08-25 20:41:17 · answer #5 · answered by grrlgenius5173 2 · 0⤊ 0⤋
The easiest way to do this problem is to draw it first. Then label all the sides accordingly. Next Use all the info you know about what you are trying to solve (i.e. how do I fid the length of the sides of triangle? HMMMM...At my stage of math I only know of one way- Pythagorean theorem). You will use this knowledge forever in math, even in graduate level mathematics.
2006-08-25 19:37:12 · answer #6 · answered by Hugh Jafro 2 · 0⤊ 0⤋
a^2 + b^2 = c^2
a = b +1
c = 4
(b+1)^2 +b^2 = 4^2 = 16
I leave it to you to figure out the details
2006-08-25 19:22:43 · answer #7 · answered by idiot detector 6 · 0⤊ 0⤋
width=2
length=1
????????
2006-08-25 19:28:59 · answer #8 · answered by skybubbles 2 · 0⤊ 0⤋
if other people do your homework for you, you'll never know if it comes up again. read a book
2006-08-25 19:23:55 · answer #9 · answered by brandoncutlip 1 · 0⤊ 0⤋