SOLUTION: How would I solve the dimensions of a rectangle if the length is 3cm more than the width and the diagonal is 15cm? I'm supposed to use factored form for the problem but I haven'

Algebra ->  Rectangles -> SOLUTION: How would I solve the dimensions of a rectangle if the length is 3cm more than the width and the diagonal is 15cm? I'm supposed to use factored form for the problem but I haven'      Log On


   

Question 925562: How would I solve the dimensions of a rectangle if the length is 3cm more than the width and the diagonal is 15cm?
I'm supposed to use factored form for the problem but I haven't been able to solve it. I know it has something to do with isolating w.
So far, I've subbed in w + 3 for the length and tried pythagorean theorem. But that answers keep coming up wrong. They should be 12 by 9.
Found 2 solutions by josgarithmetic, srinivas.g:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
w for width, L for length, d for the size of the diagonal.

A rectangle with dimensions L and w and diagonal d forms two right triangles allowing for the Pythagorean Theorem arithmetic statement w%5E2%2BL%5E2=d%5E2.

According to your example description, L=w+3 and d=15.
highlight_green%28w%5E2%2B%28w%2B3%29%5E2=15%5E2%29;
take this the rest of the way.

(You should find along the way, highlight_green%28w%5E2%2B3w-108=0%29 .)

Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
Let width be w cm
length = (w+3) cm
diagonal = 15 cm
as per pythagorean theorem
+w%5E2+%2B%28w%2B3%29%5E2+=15%5E2
+w%5E2%2B+%28w%2B3%29%2A%28w%2B3%29+=+225
+w%5E2+%2Bw%2A%28w%2B3%29%2B3%28w%2B3%29+=225
+w%5E2+%2Bw%2Aw%2Bw%2A3%2B+3%2Aw%2B3%2A3++=225
+w%5E2+%2Bw%5E2+%2B3w%2B3w%2B9+=225
+2w%5E2%2B6w%2B9+=225
move 225 to the right
+2w%5E2%2B6w%2B9-225+=0
+2w%5E2%2B6w-216=0
on dividing with 2 both sides
+w%5E2+%2B3w-108=0
+w%5E2%2B12w-9w-108=0
+w%28w%2B12%29-9%28w%2B12%29+=0
+%28w-9%29%28w%2B12%29++=0+
(w-9) =0 or (w+12 )= 0
w=9 or w=-12
w cannot be negative
so w= 9
l = w+3 = 12
so length = 12 cm
width = 9 cm