Question

AOBC is a rectangle whose vertices are A(0,3),o(0,0) and B(5,0) find the length of its diagonal
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Answer 1

${\large{\underline{\boxed{\pink{ \bf{✯ Given ✯}}}}}}$

• AOBC is a rectangle.
• Vertices are A(0,3),o(0,0) and B(5,0)

${\large{\underline{\boxed{\pink{ \bf{✯ To \: find ✯}}}}}}$

• Length of its diagonal.

${\Large{\underline{\boxed{\red{ \bf{꧁ Solution ꧂}}}}}}$

${ \sf{∴ \: Distance \: between \: the \: points \:}} \\ { \sf{ (x_1, y_1) and \: (x_2 , y_2 ).}}$

Here,

1. ${\sf{(x_1,y_1)}}$ = ${\sf{(0,3)}}$
2. ${\sf{(x_2,y_2)}}$ =${\sf{(5,0)}}$
3. o(0,0) is origin.
4. Length of AB means length of Diaginal.

So,

• Now, length of the diagonal AB = Distance between the points A(0, 3) and B(5, 0).

Formula :-

$\large{ \underline{ \boxed{ \bf{Diagonal = \sqrt{ {(x_2-x_1)}^{2} + (y_2-y_1)^{2} } }}}}$

So, according to the question:-

Substituting the values,

${ \bf{Diagonal = \sqrt{ {(0 - 5)}^{2} + (3 - 0)^{2} } }}$

${ \bf{Diagonal = \sqrt{ {( - 5)}^{2} + (3)^{2} } }}$

${ \bf{Diagonal = \sqrt{ {25+ 9 } }}}$

$\large{ \underline{ \boxed{ \blue{ \bf{AB= \sqrt{ {34 } }}}}}}$

Hence, the required length of its diagonal is √34 or length of AB is √34.

Answer 2

Hlo there !

Given:-

Vertices if the rectangle :-

• A(0,3) = (x',y')
• O(0,0)
• B(5,0) = (X",y")

To find:-

• Length if the diagonal.

Knowledge to be applied:-

• We can see that, O(0,0) is origin so, AB becomes the Diagonal.

Formula :-

$\huge \fbox \blue{diagonal=√(x' - x")²+ (y'-y")²}$

Now putting the values in the formula:-

$\implies$√(0-5)²+(3-0)²

$\implies$√25+9

$\implies$√34.

Hence, the length of the diagonal is √34 units.