Given that the diagonal is of length 13 cm, and that the width is x cm, derive the equation of x^2-17x+60=0. Hence find the dimensions of the rectangle.
2007-08-28 13:29:19 · 6 answers · asked by nidya 1 in Science & Mathematics ➔ Mathematics
Let sides be x and y
2x + 2y = 34
x + y = 17
y = 17 - x
Also
x² + y² = 13²
x² + (17 - x)² = 13²
x² + 17² - 34x + x² = 13²
2x² - 34x + 17² - 13² = 0
2x² - 34x + 120 = 0
x² - 17x + 60 = 0
(x - 12) (x - 5) = 0
x = 12 , x = 5
y = 5 , 12
Dimensions are 5 cm by 12cm
2007-08-28 19:53:51 · answer #1 · answered by Como 7 · 2⤊ 1⤋
If x = one side, then the adjacent side is (17 - x) since together they add up to half the perimeter. By the Pythagorean Theorem,
x^2 + (17-x)(17-x)= 13 ^2
Do out the FOIL: x^2 + [289 - 34x + x^2 ] = 169
Combine the x^2 and move the 169 over by subtracting it and get 2x^2 - 34x + 120 = 0
Now divide both sides by 2 and you get it.
FOIL it to solve for x.
2007-08-28 13:34:52 · answer #2 · answered by hayharbr 7 · 2⤊ 0⤋
agreed, learn this for yourself, but the answer is 5 x 12.
there are some basic triangle (half-rectangle) groupings:
3,4,5
5,12,13
8,15,17
9,40,41
since the diagonal is 13, and 5 plus 12 is 17, i assumed it works.
2007-08-28 13:33:40 · answer #3 · answered by kms107 2 · 0⤊ 1⤋
GO TO http://www.webmath.com/ for any math help......
2007-08-28 13:34:15 · answer #4 · answered by parth p 1 · 0⤊ 1⤋
lol homework already?
2007-08-28 13:32:37 · answer #5 · answered by Foxy_chicka_04 2 · 0⤊ 1⤋
is this your homework? shame!
2007-08-28 13:32:07 · answer #6 · answered by ? 5 · 1⤊ 0⤋