Question

A rectangle has length $2.4$ and width $1.8$. Find the length of a diagonal.

Short answer

The length of diagonal is $3$.

Step-by-step solution

Step 1. Given information.

The rectangle has length $2.4$ and width $1.8$.

Step 2. Concept used.

1. A Rectangle have opposite sides are equal and each interior angle is right angle.
2. Pythagoras Theorem state that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

Step 3. Now find the diagonal.

First we draw a rectangle of length $2.4$and width $1.8$and labeled $\square ABCD$.

In $\Delta ADC$.

We use Pythagoras Theorem.

$\begin{array}{l}{x}^2={1.8}^2+{2.4}^2\\ x^2=3.24+5.76\\ x^2=9\end{array}$

Taking square root we get.

$\begin{array}{c}x=\pm \sqrt{9}\\ =\pm 3\end{array}$

Since, distance is always a positive quantity so we neglect negative sign.

Therefore, the value of $x$is$3$.