SOLUTION: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Find the dime

Question 195654This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Find the dimensions of a rectangle having perimeter 14 m and a diagonal of length 5 m. This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the perimeter formula

Plug in

Divide every term by 2

Subtract W from both sides.

Rearrange the terms.

--------------------------

Move onto the Pythagorean Theorem

Plug in , , and

Plug in

Square 5 to get 25

FOIL

Subtract 25 from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for W

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the widths are or

If we plug these widths into , we'll get the lengths

or

So we'll make the length the longer dimension.

So the length is 4 m and the width is 3 m
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