A rectangle has a length that is 1 inch longer than its width. The sum of the square of its sides are 481. Find the dimensions of the rectangle. (Length and width)

Answer 1

Since you have the sum of the sides of a rectangle, 481, that is actually the square of the hypotenuse you get when the rectangle is split into two equal right triangles with a diagonal.

In short you can use the Pythagorean Theorem

Since

Length = w + 1

Width = w

We have

481 = w² + (w + 1)²

481 = w² + w² + 2w +1

You can form a quadratic by moving everything over to one side

0 = 2w² + 2w + 1 - 481

0 = 2w² + 2w - 480

Divide both sides by 2

0 = w² + w - 240

Factoring gives

0 = (w + 16)(w - 15)

Since the Width, w has to be positive

w = 15 is the only useful value

L = w +1 = 15 + 1 = 16

Length = 16

Width = 15

Checking against the sum of their squares

481 = 16² + 15²

481 = 256 + 225

481 = 481

I hope you find this useful

Answer 2

let w be the width.

Then we can define the length as 1 + w (1 inch longer than width)

The sum of the square of its sides are 481, so

(w)² + (1+w)² = 481

w² + 1 + 2w + w² = 481

2w² + 2w - 480 = 0

w² + w - 240 = 0

Use guess with the factors of 240, use quadratic formula, or graph the equation to find w:

w = 15 inches

so the length is 16 inches