Question

A field is in the shape of a rhombus whose one of the diagonals measures 40 m and the area is 500 m square . find the length of the other diagonal . Also find the cost of ploughing the field at Rs. 2.50 per square metre​

Answer 1

Given:

• Diagonal of rhombus = 40m
• Area of rhombus = 500m²
• Cost of ploughing 1m² = rs. 2.50

Find:

• Length of the other diagonal = ?
• Cost of ploughing the field = ?

Solution:

Here,

we, know that

$\underline{\boxed{\red{\sf Area \: of \: Rhombus = \frac{1}{2}\times(d_{1} \times d_{2})}}}$

where,

Area of Rhombus = 500m²

$\sf d_1=40m$ = 40m

So,

$\sf\to Area \: of \: Rhombus = \frac{1}{2}\times(d_{1} \times d_{2})$

$\sf\to 500 =\frac{1}{2}\times(40 \times d_{2})$

$\sf\to 500=20d_{2}$

$\sf\to\frac{500}{20}= d_{2}$

$\sf\to d_{2} = 25m$

$\sf Hence,\underline{\boxed{\sf d_{2} = 25m}}$

Now,

Cost of ploughing the 1m² of the field = rs.2.50

So, Cost of ploughing 500m² of the field = 500×2.50

=rs. 1250

$\sf Hence,\underline{\boxed{\sf cost \: of \: ploughing \: the \: field =rs.1250}}$

Answer 2

GIVEN :-

• diagonal of rhombus (D1) = 40 m.
• Area of rhombus = 500 m².
• Cost of plugging the field = Rs. 2.50 /m².

TO FIND :-

• The other diagonal (D2) .
• Total cost of ploughing the field.

SOLUTION :-

$\\ \\ : \implies \displaystyle \sf Area \: of \: rhombus = \dfrac{1}{2} \times D_{1} \times D_{2}$

$: \implies \displaystyle \sf500 = \dfrac{1}{2} \times 40 \times D_{2}$

$: \implies \displaystyle \sf500 = 20 \times D_{2}$

$: \implies \underline{ \boxed{ \displaystyle \sf D_{2} = 25 \: m.}} \: \: \: \: \: \: \: \: \bigg \lgroup\displaystyle \sf Other \ Diagonal \bigg \rgroup$

___________________

$\\ \\ \dashrightarrow \displaystyle \sf cost \ of \ ploughing \ = 500 \times 2.50$

$\dashrightarrow\underline{ \boxed{\displaystyle \sf cost \ of \ ploughing = 1250}}$

$\therefore \underline {\displaystyle \sf Cost \ of \ pluoghing \ the \ field \ is \ Rs. 1250}$