91影视

A conditional statement is false when the hypothesis is true but the conclusion is false.

The area of a rectangle is given as $A=lw$, where $A$is the area,$l$is the length and $w$is the width of the rectangle.

The given statement is 鈥淚f the length of a rectangle is doubled, then the area of the rectangle is doubled.鈥�

Then the hypothesis is 鈥渓ength of a rectangle is doubled鈥� and the conclusion is 鈥渁rea of the rectangle is doubled鈥�.

Let the hypothesis be true. So, the length of a rectangle is doubled.

Then, $l_{new}=2l$.

Put $l_{new}=2l$ in $A=lw$ to get,

$\begin{array}{l}{A}_{new}=l_{new}w\\ =2lw\\ =2\left(lw\right)\\ =2A\end{array}$

So, $A_{new}=2A$.

This implies that the area of the new rectangle is double that of the area of the initial rectangle.

So, the conclusion is true.

It has been obtained that if the hypothesis is true, then the conclusion is true. This implies that the given statement is true.