Math help?

Question

a rectangle is five times as long as it is wide. If it were 34 cm shorter and 24 cm wider, it would be a square. what are the dimensions?

Answer 1

l= 5w
If it becomes a square then
5w-34 = w+24
4w = 58
w = 14.5cm
so l = 72.5cm

Answer 2

It's been awhile since I've done math, so not sure if this is right....

Dimensions of the rectangle would be length (l) times width (w)...making it 5w x w; the dimensions of the square would then be 5w-34 and w+24. Since it's a square we're trying to make, those two would then be equal... 5w-34 = w + 24.

5w - 34 = w + 24 (Add 34 to both sides)
5w = w + 58 (Subtract w from both sides)
4w = 58 (Divide both sides by 4)
w = 14.5

If you go back and check it....then if the width is 14.5 cm, that would make the length (5w) 72.5 cm....add 24 cm to the width and that gives you 38.5 cm, subtract 34 from the length, and that gives you 38.5 cm. as well, making it a square....

Answer 3

The formula is 5w -34 = w + 24 thus 4w = 58 thus w = 14.5 thus the rectangle is 72.5cm l and 14.5 cm w. 72.5 - 34 =38.5 and 14.5 + 24 = 38.5.

Answer 4

Rectangle has sides with lengths x wide and y long, so from the first sentence:
5*x=y
If it's a square, both sides are equal, giving this equation from the second sentence:
x+24=y-34
Simplifying the last equation gives:
x=y-58
Substituting the first equation into the last equation:
x=5x-58
4x=58
2x=29
x=14.5
y=x+58; y=14.5+58
y= 72.5
So the rectangle is 14.5 wide and 72.5 long

Answer 5

This develops two equations:
L = 5W
L-34 = W+24
Making the obvious substitution:
5W-34 = W+24
4W = 58
W = 14.5; L = 72.5.

Answer 6

Let x be width.
B=x
Length L=5x
L-34=B-24 since it would be square
5x-34=x+24
4x=58
x=14.5 cm

Length = 5x=5*14.5=72.5 cm

Length & Breadth are 72.5 cm & 14.5 cm respectively.

Answer 7

L = 5W
L-34 = W + 24

5W - 34 = W + 24
4W = 58
W = 14.5cm
L = 72.5cm

Answer 8

do your own homework!