Question

California.Mathematics Group Superstar
The perimeter of rectangular picture is 86 inches .Twice the width exceeds the length by 2 inches.What is the dimensions of the picture?

Answer 1

2w+2=l, 2l+2w=86

so far so good?

Answer 2

Okay, the perimeter p = 86 = twice the length l plus twice the width w, so p = 2l + 2w - 86. We're given that twice the width is 2 more than the length, so 2w = l + 2, or l = 2w - 2. Then we can substitute this in to get p = 2l + l + 2 = 86, or 86 = 3l + 2, or 3l = 84, or l = 28. Then we have 86 = 2*(28) + 2w, so 2w = 30, or w = 15. Thus, (l,w) = (28,15).

Answer 3

*p = 2l + 2w = 86

Answer 4

now I see it, but how is it 2w-2=l instead of 2w+2=l?

Answer 5

Twice the width is 2 more than the length, so 2w = l + 2. From there you can just rewrite it to 2w - 2 = l.

Answer 6

ok, thanks. I see that they are a pair of linear equations now. So now you just find the intersect?

Answer 7

Well, I solved it by using substitution, but the two techniques are mathematically equivalent, so you could solve it by finding the intersect.

Answer 8

I solve w=15

Answer 9

ty Liort and Blacksteel