The length and width of a rectangle are 48 inches and 40 inches. To the nearest inch, what is the length of its diagonal?
Since rectangles have right angles, we can use the Pythagorean Theorem here.
Let's call this rectangle \(CATS\), where \(CA = 40\), \(AT = 48, TS = 40, \)and \(CS = 48\) inches.
The diagonals are \(CT\) and \(AS\).
A right triangle is formed by \(CA, CT, \) and \(AT\), with legs of \(48 \) inches and \(40 \) inches. The length of the hypotenuse is what we want to find.
Let's call the length of \(CT\) "\(d\)".
Using the Pythagorean Theorem, \(48^2 + 40^2 = d^2\).
\(48^2 = 2304\)
\(40^2 = 1600\)
\(d^2 = 2304 + 1600\)
\(d^2 = 3904\)
\(d = \) the square root of \(3904\)
\(d\) inches, to the nearest inch, is \(62\) inches.
ANSWER: \(62\) inches.
I hope this is helpful,