Question

The diagonal of a rhombus are 5.2cm and 8.5cm , respectively. A parallelogram equal in area to this rhombus has one of its parallel sides 5cm . Find the corresponding altitude .​

Answer 1

$\bf{\Huge{\underline{\boxed{\bf{\red{ANSWER\::}}}}}}$

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

The diagonal of a rhombus are 5.2cm & 8.5cm respectively. A parallelogram equal in area to this rhombus has one its parallel side is 5cm.

$\bf{\Large{\underline{\sf{\violet{To\:find\::}}}}}$

The corresponding altitude of parallelogram.

$\bf{\Large{\underline{\sf{\blue{Explanation\::}}}}}$

We know that formula of the area of rhombus:

→ $\bf{\frac{1}{2} *D1*D2}$   [sq.units]

$\bf{We\:have\begin{cases}\sf{The\:first\:diagonal\:of\:rhombus[D1]=5.2cm}\\ \sf{The\:second\:diagonal\:of\:rhombus[D2]=8.5cm}\end{cases}}$

So,

$\longmapsto\bf{Area=\frac{1}{2} *D1*D2}$

$\longmapsto\bf{Area=\frac{1}{2} *5.2cm*8.5cm}$

$\longmapsto\bf{Area=(\frac{1}{\cancel{2}} *\cancel{5.2}*8.5)cm^{2}}$

$\longmapsto\bf{Area=(2.6*8.5)cm^{2} }$

$\longmapsto\bf{Area=22.1cm^{2} }$

We know that area of parallelogram: (Base × Height)    [sq.units]

A/q

→ Area of parallelogram = Area of rhombus

→ $\bf{Base*Height=\frac{1}{2} *D1*D2}$

→ 5cm × Height = 22.1cm²

→ Height = $\bf{\cancel{\frac{22.1cm^{2} }{5cm} }}$

→ Height = 4.42cm

Thus,

The corresponding altitude is 4.42cm.

Answer 2

Question :

The diagonal of a rhombus are 5.2 cm and 8.5 cm, respectively. A parallelogram equal in area to the rhombus, has one of its parallel sides 5 cm . Find the corresponding altitude .

Solution :

$\underline{\bold{Given :}}$

• First diagonal of the rhombus = 5.2 cm
• Second diagonal of the rhombus = 8.5 cm
• Base of the parallelogram=5 cm

$\underline{\bold{To\:Find:}}$

• The corresponding altitude of the parallelogram.

$\because{Area\:of\:the\:parallelogram =Area\:of\:the\:rhombus}$

$\boxed{\purple{Area\:of\:rhombus=\frac{1}{2} \times Product \: of \: its \: diagonals}}$

$\implies Area\:of\:the\:rhombus=\frac{1}{2} \times Product \: of \: its \: diagonals\\\implies Area\:of\:the\:rhombus=\frac{1}{2} \times (5.2\:cm\times 8.5\:cm)\\\implies Area\:of\:the \:rhombus=\frac{1}{2} \times 44.2\:cm^2\\\implies Area\:of\:the\:rhombus=22.1\:cm^2$

$\therefore{Area\: of\:the\: parallelogram=22.1\:cm^2}$

$\rule {193}{1}$

$\boxed{\blue{Area\:of\: parallelogram =Base \times Height}}$

$\implies Area \:of\:the \: parallelogram =Base \times Height\\\implies 22.1\:cm^2=5\:cm \times Height\\\implies \frac {22.1\:cm^2}{5\:cm}=Height\\\implies 4.42\:cm =Height\\\implies Height=4.42\:cm$

$\boxed {\green{\therefore{The\: corresponding\: altitude \:of\:the\: parallelogram=4.42\:cm}}}$