Question

The area of a rhombus is 2140m² and one of its diagonals is 164m.find the length of the other diagonal. given correct answer.

Answer 1

$\bf{Answer\colon}$

Formula of Area of Rhombus =
$\frac{1}{2}\times\:Product\:of\:its\:diagonals$

Given Area = 2140 $m^2$
Length of 1 Diagonal(p) = 164 m

We have to find the length of 2nd Diagonal. Let it be q.

Therefore,
Area of Rhombus = 2140$m^2$

$\frac{1}{2}\times\:p\times\:q$ = 2140

$\frac{1}{2}\times\:164\times\:q$ = 2140

$164\times\:q\:=\:2140\times\:2$

$q\:=\:\frac{2140\times\:2}{164}$

$q\:=\:26.097(approx.)$

Hence, Required answer is 26.097m.

Answer 2

Solutions :-

We have,

Area of Rhombus = 2140 m²
Diagnol = 164 m

Let the length of other diagonal be x

Now,
Find the length of the other diagonal :-

We know the formula,

$Area \:of \:Rhombus \\ = \frac{1}{2} \times diagonal1 \times diagonal2$

A/q

$= > 2140 = \frac{1}{2} \times 164 \times x \\ \\ = > 2140 = 82 \times x \\ \\ = > x = \frac{2140}{82} = 26.09 \: approx.$


Answer : The length of the other diagonal is 26.09 m