Question

The base of a triangle is 24 cm and tye corresponding altitude is 16 cm.The area of the rhombus is equal to the area of the triangle.If one of the diagonals of the rhombus is 20 cm, find tye length o the other diagonal

Answer 1

$\huge{\mathbb{\purple{\underline{Solution:-}}}}$

Given:-

Area of triangle = Area of rhombus

$area \: of \: triangle = \frac{1}{2} \times base \times height$

$= \frac{1}{2} \times 24 \times 16$

$= 192 \: cm ^{2}$

$area \: of \: rhombus \: = \frac{1}{2} \times products \: of \: diagonal$

$= \frac{1}{2} \times diagonal1 \times diagonal2$

$192 = \frac{1}{2} \times 20 \times diagonal2$

$192 = 10 \times diagonal2$

$\frac{192}{10} = diagonal2$

$19.2 \: cm \: = diagonal2$

$so \: the \: length \: of \: other \: diagonal \: is \: 19.2 cm$

$\huge\mathfrak{Thanks........... ..}$

Area of rhombus

Answer 2

$<b>$
$<u>Given</u>$ :- Base of Triangle is 24 cm,

Altitude of Triangle is 16 cm, and

Area of Triangle = Area of Rhombus.

$<u>According To Question :-</u>$

Area of Triangle = $\dfrac{1}{2}$ × b × h

= $\dfrac{1}{2}$ × 24 × 16

$= {192\ cm}^{2}$

Area of Rhombus = $\dfrac{1}{2}$ × d1 × d2

= 192 = $\dfrac{1}{2}$ × 20 × d2

= 192 × 2 × $\dfrac{1}{20}$ = d2

= 19.2 cm

So, the length of other diagonal of Rhombus is $\boxed{19.2 \ cm}$