Question

Quadrilateral $ABCD$ is a rectangle whose three vertices are $B(4,0),C(4,3)$ and $D(0,3)$. Find the length of its diagonals.

Answer 1

Given $ABCD$ is a rectangle

From the diagram vertices of $A$ will be $(0,0)$

$BDandAC$ are diagonals of the rectangle.

Let,

$A=(0,0)$ $=(x_1,y_1)$

$B=(4,0)$ $=(x_2,y_2)$

$C=(4,3)$ $=(x_3,y_3)$

$D=(0,3)$ $=(x_4,y_4)$

$BD=\sqrt{(x_4-x_2{)}^2+(y_4-y_2{)}^2}$

$=\sqrt{(0-4{)}^2+(3-0{)}^2}$

$=\sqrt{16+9}$

$=\sqrt{25}$

$BD=\sqrt{\left(25\right)}$

$BD=5$ units

In a rectangle, diagonals are equal.

$\therefore AC=BD=5$ units.