Question

$\huge\underline\mathfrak\pink{➡️question⬅️}$

find the area of a rhombus whose sides is 5 cm and whose altitude is 4.8cm. if one of its diagonal is 8 cm long, find the length of the other diagonal.

give relevant answer..
:)​

Answer 1

Step-by-step explanation:

HOPE IT HELP'S.......

Answer 2

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the Concept of Areas of Rhombus has been used. We see we are given one diagonal of the rhombus as well as the base and height. We know that Rhombus is a parallelogram so we can calculate its area using the area of Parallelogram. Then we have the method to calculate area of rhombus using diagonals. Using these both, we can find the value of another diagonal.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{\pink{Area\;of\;Rhombus\;=\;\bf{Base\;\times\;Height}}}}$

$\\\;\boxed{\sf{\pink{Area\;of\;Rhombus\;=\;\bf{\dfrac{1}{2}\;\times\;(Product\;of\;Diagonals)}}}}$

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★ Solution :-

Given,

» Altitude of Rhombus = H = 4.8 cm

» Base of Rhombus = B = 5 cm

» First diagonal of Rhombus = D₁ = 8 cm

• • Let the second diagonal of the rhombus D₂ be 'x'.

We know that,

$\\\;\sf{:\rightarrow\;\;Area\;of\;Rhombus\;=\;\bf{Base\;\times\;Height}}$

Also,

$\\\;\sf{:\rightarrow\;\;Area\;of\;Rhombus\;=\;\bf{\dfrac{1}{2}\;\times\;(Product\;of\;Diagonals)}}$

Combining these both, we get,

$\\\;\sf{:\Longrightarrow\;\;\dfrac{1}{2}\;\times\;(Product\;of\;Diagonals)\;=\;\bf{Base\;\times\;Height}}$

By applying values, we get

$\\\;\sf{:\Longrightarrow\;\;\dfrac{1}{2}\;\times\;(D_{1}\;\times\;D_{2})\;=\;\bf{B\;\times\;H}}$

$\\\;\sf{:\Longrightarrow\;\;\dfrac{1}{2}\;\times\;(8\;\times\;x)\;=\;\bf{5\;\times\;4.8}}$

$\\\;\sf{:\Longrightarrow\;\;\dfrac{1}{2}\;\times\;8\;\times\;x\;=\;\bf{24}}$

$\\\;\sf{:\Longrightarrow\;\;4\;\times\;x\;=\;\bf{24}}$

$\\\;\sf{:\Longrightarrow\;\;x\;=\;\bf{\dfrac{24}{4}}}$

$\\\;\sf{:\Longrightarrow\;\;x\;=\;\bf{\red{6\;\;cm}}}$

$\\\;\underline{\boxed{\tt{Hence,\;\:length\;\:of\;\:another\;\:diagonal\;\:=\;\bf{\purple{6\;\;cm}}}}}$

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$\\\;\underline{\underline{\rm{\gray{Properties\;of\;Rhombus\;::}}}}$

• Opposite Sides are equal of Rhombus.

• Diagonals bisect each other at 90° of a Rhombus.

• Opposite Sides are parallel to each other in a Rhombus.

• Square and Rectangle are a type of Rhombus but a Rhombus is not a square of rectangle.

• Sum of adjacent angles = 180° in a Rhombus.