Question

Plzzzzz..... Answer. U will get 30 points.
Find the area of a rhombus whose side is 5 cm and its altitude is 4 cm. If one of its diagonal is 8 cm, find the length of the other diagonal.

Plzzz answer, I will mark u the brainliest also

Answer 1

Answer:

5cm

Step-by-step explanation:

Area of the rhombus = Side × Length of the altitude 

= 5*4

= 20 sq cm 

Now,

Let the length of the other diagonal = x

It is known that the area of a rhombus is half the product of its diagonals. 

∴ (1/2) × 8 × x = 20

⇒ 4x = 20

⇒ x = 5 cm

The length of the other diagonal is 5 cm.

PLEASE MARK BRAINIEST

Answer 2

AnswEr :

$\bf{\green{\underline{\underline{\bf{Given\::}}}}}$

A rhombus whose side is 5 cm and it's altitude is 4 cm.If one of it's diagonal is 8 cm long.

$\setlength{\unitlength}{1.2cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\large{A}}\put(7.7,0.9){\large{B}}\put(9.2,0.7){\large{\sf( 5\:cm)}}\put(11.1,0.9){\large{C}}\put(9.9,2.1){\large{O\:(8cm)}}\put(8,1){\line(1,0){3}}\put(11,1){\line(1,2){1}}\put(9,3){\line(3,0){3}}\put(11.7,2){\large{\sf(4\:cm)}}\put(11,1){\line(-1,1){2}}\put(8,1){\line(2,1){4}}\put(8,1){\line(2,1){4}}\put(8,1){\line(1,2){1}}\put(12.1,3){\large{D}}\end{picture}$

$\bf{\green{\underline{\underline{\bf{To\:find\::}}}}}$

The area of rhombus and the length of the other diagonal.

$\bf{\green{\underline{\underline{\bf{Explanation\::}}}}}$

$\bf{We\:have}\begin{cases}\sf{Altitude\:of\:\triangle BCD=4\:cm}\\ \sf{Base\:of\:the\: \triangle BCD=5\:cm}\\ \sf{Diagonal\:of\:rhombus\:(d_{1})=8\:cm}\end{cases}}$

Formula use :

$\bf{\boxed{\bf{Ar.\:of\:triangle=\frac{1}{2} \times base\times height}}}}}$

$\leadsto\sf{\red{Area\:of\:rhombus=2\times area\:of\: \triangle BCD}}\\\\\\\leadsto\sf{Area\:of\:rhombus=\cancel{2}\times \dfrac{1}{\cancel{2}} \times 5\times 4}\\\\\\\leadsto\sf{Area\:of\:rhombus=5\times 4}\\\\\\\leadsto\sf{\pink{Area\:of\:rhombus=20\:cm^{2} }}$

Now;

$\bf{\boxed{\bf{Area\:of\:rhombus\:=\:\frac{1}{2} \times d_{1}\times d_{2}}}}}$

$\mapsto\sf{20\:cm^{2} =\dfrac{1}{\cancel{2}} \times \cancel{8\:cm}\times d_{2}}\\\\\\\mapsto\sf{20\:cm^{2} =4\:cm\times d_{2}}\\\\\\\mapsto\sf{d_{2}=\cancel{\dfrac{20cm^{2} }{4cm} }}\\\\\\\mapsto\sf{\pink{d_{2}=5\:cm}}$

Thus;

The area of rhombus is 20 cm² and other diagonal of rhombus is 5 cm.