The perimeter of a rectangle is 70 and its diagonal is 25. find the length and width?

Question

please be specific and try and give step by step description. ty

Answer 1

p = 70 = 2L +2W

d = 25

L^2 + W^2 =d^2 =625

L + W = 35

L^2 + (35 - L)^2 = 625

L^2 +35^2 - 70L +L^2 = 625

2L^2 - 70L +35^2 -625 = 0

2L^2 - 70L +600 = 0

Use quadratic formula to get L = 15 or 20.

Thus length and width are 15 and 20.

Answer 2

2x + 2y = 70
x^2 + y^2 = 625

Start with first equation:

2x + 2y = 70
2y = 70 - 2x
y = 35 - x = -x + 35

Now plug it in to second equation:

(-x + 35)^2 + x^2 = 625
x^2 - 70x + 1225 + x^2 = 625
2x^2 - 70x + 1225 = 625
2x^2 - 70x + 600 = 0

Now I use the quadratic formula here:

x = (-b +/- sqrt(b^2-4ac))/2a

Too long to write it all out here, but you get the solutions:

x = 20 or 15

Width = 15, Length = 20

Answer 3

Make x = width and y = length

1. 2x + 2y = 70
and
2. x^2 + Y^2 = 25

From 1 get x then sub into 2. Find value of y and then sub into 1.

I think.......