Question

The diagonals of a rhombus are in ratio 3:4 if the longer diagonal is 12cm then find the are of rhombus​

Answer 1

The area of a rhombus = 54 cm².

Given :

The ratio of the diagonal of a rhombus = 3 : 4.

The length of the longer diagonal = 12 cm.

To Find :

The area of a rhombus.

Solution :

Let,

The smaller diagonal of a rhombus be 3x.

The longer diagonal of a rhombus be 4x.

We know that,

$\gray{ \boxed{ \orange{ \tt{Area \: of \: a \: rhombus = \dfrac{1}{2} \times d_{1} \times d_{2} }}}} </p><p>$

First, we need to find the smaller diagonal of a rhombus.

Given,

The longer diagonal of a rhombus = 12 cm

That means,

$\begin{gathered} \implies4x = 12 \: cm \\ \\ \implies x = \cancel\dfrac{12}{4} \: cm \\ \\ \implies x = 3 \: cm \end{gathered} </p><p>$

Hence, the value of x is 3 cm.

So,

The smaller diagonal of a rhombus = 3x

$\begin{gathered} \implies 3(3 \: cm) \\ \\ \implies3 \times 3 \: cm \\ \\ \implies9 \: cm\end{gathered} </p><p>$

Hence, the diagonals of a rhombus are 12 cm and 9 cm

Now we have,

$</p><p>\sf d_{1} = 9 \: cm$

$</p><p>\sf d_{2} = 12 \: cm$

Now, substitute both the values of the diagonals in the formula of the area of a rhombus.

$\begin{gathered} \implies \dfrac{1}{ \cancel2} \times 9 \: cm \times \cancel{12} \: cm \\ \\ \implies1 \times 9 \times 6 \: {cm}^{2} \\ \\ \implies54 \: {cm}^{2} \end{gathered} </p><p>$

Hence,

The area of a rhombus is 54 cm².

Answer 2

Step-by-step explanation:

Case Study 3:

Baluchari Sari is a type of sari, a garment worn by women in Bangladesh and Indian States of West Bengal. This particular type of sari originated in West Bengal and is known for depictions of mythological scenes on the pallu of the cari In this wedding season shopkeepers are giving big discounts on the marked price of the sarees

A shopkeeper allows 25% discount on the marked price of the sarees and still makes a profit of 20%. If he gains 225 over the sale of one saree.

On the basis of above information answer the following questions

(a) Find the cost price of the sareeheat capacity, ratio of heat absorbed by a material to the temperature change. It is usually expressed as calories per degree in terms of the actual amount of material being considered, most commonly a mole (the molecular weight in grams). The heat capacity in calories per gram is called specific heat