Question

find the area of a rhombus whose side is of length 5m and one of it's diagonals is of length 8m.​

Answer 1

Answer:

Answer

Area of rhombus = Base × Height =

2

1

×Product of diagonals

⇒5×4.8=

2

1

×(8×x)

⇒24=

2

1

×(8×x)

⇒x=6 cm

Answer 2

$\underline{\underline{\maltese\: \: \textbf{\textsf{ Question }}}}$

★ The length of side of a rhombus is 5m and one of its diagonal is 8 m. Then what is the length of the other diagonal?

$\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

Length of the side of the rhombus = 5 m

Length of the diagonal of the rhombus = 8 m

We know that :-

$\tt{The\:diagonals\:of\:rhombus\:bisect\:each\:other\:at\:right\:angles.}$

Due to that property, the half of the other diagonal will be :-

By the Pythagoras Theorem:-

$\implies \tt{H^{2} = P^{2} + B^{2}} \\ \\ \implies \tt{5^{2} = 4^{2} + x^{2}} \\ \\ \implies \tt{25 - 16 = x^{2}} \\ \\ \implies \tt{9 = x^{2}} \\ \\ \implies \tt{x = 3 m}$

Now, that we have the half of the length of the other diagonal, we can say that the length of the diagonal = 3 × 2 (m) = 6m