Question

using Pythagoras Theorem, find the length of the second diagonal of a rhombus of side 5 cm and having one side of its diagonal as 8cm.

Answer 1

hope it will help you!!

Answer 2

The length of second diagonal of rhombus is 6 cm

Solution:

Given:

The figure for this sum is attached below

AC and BD are the diagonals

Length of side of Rhombus = 5cm and one diagonal is 8cm .i.e Let AC = 8

Since in Rhombus the diagonal bisect each other and also at right angle

$\text { Therefore, } \frac{A C}{2}=A O=4 \mathrm{cm}$

Also AB = 5cm (Given)

In Triangle AOB, using Pythagoras Theorem

$\begin{array}{l}{\mathrm{AO}^{2}+\mathrm{BO}^{2}=\mathrm{AB}^{2}} \\\\ {4^{2}+\mathrm{BO}^{2}=5^{2}} \\\\ {\mathrm{BO}^{2}=25-16=9} \\\\ {\mathrm{BO}=\sqrt{9}=3 \mathrm{cm}} \\\\ {\text {Also, } \mathrm{BD}=2 \times \mathrm{BO}=2 \times 3=6 \mathrm{cm}}\end{array}$

Hence , the length of other diagonal is 6 cm

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