Question

Draw a rhombus ABCD. if AC= 6cm and AB=5cm, find the length of BD.​

Answer 1

(refer to the attachment)

• GIVEN:-

AC (1st diagonal) = 6 cm

AB = 5 cm

• To Find:-

Length of BD ( other diagonal).

• SOLUTION:-

We know that in a rhombus, diagonals bisect each other at right angles.

So by applying Pythagoras theorem,

$\large{\sf {(hypo)}^{2} = {(side)}^{2} + {(base)}^{2} }$

where,

hypotenuse = hypo,

side = s,

base = b.

$\large{\sf {(AB)}^{2} = {(AO)}^{2} + {(BO)}^{2}}$

$\large{\sf = > {(25)}^{2} = {(3)}^{2} + {(BO)}^{2}}$

$\large{\sf = > 25 = 9 + {(BO)}^{2} }$

$\large{\sf = > 25 - 9 = {(BO)}^{2}}$

$\large{\sf = > 16 = {(BO)}^{2}}$

Now by square rooting both sides,

$\large{\sf => \sqrt{16} = BO}$

$\large{\sf =>BO \: = \frac{ + }{ - } 4 \: }$

Length of BO = 4 cm

Therefore Length of BD = 2 × 4 = 8 cm.

$\large\red\therefore\boxed{\sf{\red{Length\:of\:BD\:=\:8\:cm.}}}$

Answer 2

Answer:

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