SOLUTION: Would someone please show the solution to this word problem step by step. Thank you. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4

Algebra ->  Rectangles -> SOLUTION: Would someone please show the solution to this word problem step by step. Thank you. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4      Log On


   

Question 87998: Would someone please show the solution to this word problem step by step. Thank you.
The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm. What are the dimensions (the length and the width) of the rectangle?
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonal of the rectangle forms the hypoteneuse of a right triangle with the legs of said triangle being the length and the width of the rectangle. Wow, that
was a mouthful. Anyways, they give you that l=w+1. So you can use the pythagorean theorem to write an equation for w:
%28w%2B1%29%5E2%2Bw%5E2=4%5E2
Square the binomial and simplify the right hand side:
w%5E2%2B2w%2B1%2Bw%5E2=16
Put the quadratic in standard form and combine like terms:
2w%5E2%2B2w-15=0
Use the quadratic formula:
w=%28-2%2B-sqrt%28%284-%284%2A2%2A%28-15%29%29%29%29%29%2F4
Simplify:
w=%28-2%2B-sqrt%28%284-%28-120%29%29%29%29%2F4
w=%28-2%2B-sqrt%28124%29%29%2F4
You need to have a positive value for the width, so throw away the negative result:
w=%28-2%2B%282%29%2Asqrt%2831%29%29%2F4
Simplify a little more:
highlight%28w=%28-1%2Bsqrt%2831%29%29%2F2%29
You can plug this into your calculator if you need a numerical value.
from the given information, l is just 1+w.
Good Luck,
tutor_paul@yahoo.com