Question

Suppose you want to build a rectangular sandbox where the width is 7 less than the length and the diagonal is 2 feet longer than the length. What are the dimensions of the sandbox?

Answer 1

The dimensions of the sandbox will be 15 feet by 8 feet.

Explanation:

Suppose we want to build a rectangular sandbox where the width is 7 less than the length and the diagonal is 2 feet longer than the length.

If x is the length and y is the width in feet, then we have the equations

x - y = 7 ......... (1) and

`\sqrt{x^(2) + y^(2)} - x = 2` ........ (2)

Now, solving equations (1) and (2) we get

`\sqrt{x^(2) + (x - 7)^(2)} - x = 2`

⇒
`\sqrt{x^(2) + (x - 7)^(2)} = x + 2`

Now, squaring both sides we get,

x² + x² - 14x + 49 = x² + 4x + 4

⇒ x² - 18x + 45 = 0

⇒ (x - 15)(x - 3) = 0

⇒ x = 15 or 3

But from equation (1) x ≠ 3, then x = 15 and y = x - 7 = 8

Therefore, the dimensions of the sandbox will be 15 feet by 8 feet. (Answer)