Question

ABCD is a rectangle whose three vertices are B (4,0), C (4,3) and D (0, 3). The length of one of its diagonals is
(a)5
(b)4
(c)3
(d)25

Answer 1

Answer:

The length of the diagonal BD is 5 units.

Among the given options option (a) 5 units is the correct answer.

Step-by-step explanation:

Given :  

ABCD is a rectangle whose three vertices are B (4,0), C (4,3) and D (0, 3).  

In Rectangle ABCD , BD is a diagonal .

By Using Distance Formula , we find the length of the diagonal BD.

In BD , x1 = 4, x2 = 0 , y1 = 0 , y2 = 3

BD = √(x2 - x1)² + (y2 - y1)²

BD = √(0 - 4)² + (3 - 0)²

BD = √4² + 3²

BD = √16 + 9

BD = √25

BD = 5 units  

Length of the diagonal BD = 5 units  

Hence, the length of the diagonal BD is 5 units.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\huge\underline\mathcal\blue{Answer}$

The correct ans is option (a) .

The length of one of its diagonal is 5 cm .

$\huge\underline\mathcal\blue{Explanation}$

It is given that ABCD is a rectangle , then BD is diagonal .

Given :

B (4,0)

=> here 4 = x1

and 0 = y1

D (0, 3)

=> here 0 = x2

and 3 = y2

So , by using distance formula we can fid the distance between BD .

Distance formula

$= \sqrt{ ({x2 - x1})^{2} + ( {y2 - y1})^{2} }$

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

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

$= \sqrt{16 + 9}$

$= \sqrt{25}$

$= 5$

Hence , the length of one of the diagonal of rectangle ABCD is 5 cm .