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.