What is the length of a rectangle is 1cm longer that its width. If the diagonal of the rectangel is 4cm, what are the dimenstions (the length and the width) of the rectangle?
2007-08-11 09:25:03 · 3 answers · asked by SunShine 1 in Science & Mathematics ➔ Mathematics
Width = x
Length = x + 1
Now use the Pythagorean Theorem
x^2 + (x + 1)^2 = 4^2 [the diagonal is the hypotenuse]
x^2 + (x^2 + 2x + 1) = 16
2x^2 + 2x - 15 = 0
a = 2, b = 2 c = -15
Plus these into the quadratic formula (which is too difficult to type into this medium)
[-2 +/- SQRT (124)]/4 = [-2 +/- 11.1]/4 = 9.1/4 or -13.1/4 = 2.275 (negative makes no sense)
width = 2.275 cm
length = 3.275 cm
2007-08-11 09:45:05 · answer #1 · answered by JM 4 · 0⤊ 1⤋
Yes, Let width = w
l=1+w
l^2 + w^2 = 4 now plug in for l to get:
4 = (w+1)^2 + w^2
4= w^2 + 2w + 1 + w^2 so
2w^2 + 2w + 1 - 4 =0
2w^2 + 2w - 3 = 0
then use quadratic formula a=2 b=2 c= -3
2007-08-11 09:37:42 · answer #2 · answered by 037 G 6 · 0⤊ 1⤋
l = w+1
l^2 + w^2 = 2
(w+1)^2 + w^2 = 2
(w+1)(w+1)+w^2=2
w^2+2w+1+w^2=2
2w^2+2w+1=2
2w^2+2w-1=0
Use the quadratic formula now to find the roots.
2007-08-11 09:33:41 · answer #3 · answered by de4th 4 · 0⤊ 3⤋