Question

10. Each side of a rhombus is 10 cm long and one of its diagonals measures
16 cm. Find the length of the other diagonal.​

Answer 1

Answer:

each side of rhombus is 10cm.

diagonal is 16cm.

Diagonal is bisected so it is 8 and rhombus at center is 90^0

then by Pythagoras theorem

8 ^2+x=10^2

x=100-64

x=root 36then x=6

then another diagonal measure 12cm

Answer 2

Answer:

Question:-

1. Each side of a rhombus is 10 cm long and one of its diagonals measures  16 cm.  Find the length of the other diagonal and hence find the area of the rhombus.

To find,

• The area of rhombus
• And the diagonal

Solution:-

━☆ AC = 16cm

━☆ AO = OC = 8cm

Diagonal of rhombus bisect each other at 90 degree

   In $\triangle$ AOB,

                     ━☆    $\rm (AB^{2} )=(AO^{2} )+(OB^{2} )$

                     ━☆    $\rm (OB^{2} )= (10^{2})-(8^{2} )$

                     ━☆      $\rm 100-64=36$

                     ━☆     BD = 2OB = $\rm 2 \times 6=12cm$

Area of rhombus = $\rm \frac{1}{2} \times d_1 \times d_2$

                             = $\rm \frac{1}{2} \times 16 \times 12= 96cm^{2}$