Question

find the diagonals of a rhombus whose area is 216 metre square and the diagonals are in the ratio 4 is to 3​

Answer 1

Understanding the Question :

The question says that the area of a rhombus is 216 m² and the diagonals of the rhombus is given in the ratio i.e. 4:3.

Thus we have to find the diagonals of the rhombus.

Given :

• Area of rhombus = 216 m²
• Diagonals = 4 : 3

To find :

• The diagonals

Solution :

Let us consider the,

$\sf{Diagonal_1=4x}$

And, $\sf{Diagonal_2=3x}$

Now,we know that the formula to find the area of rhombus is :

$\boxed{\text{\sf{\red{Area of rhombus=pq/2}}}}$

Here p and q are the diagonals of the rhombus.

Putting the values :

$\mapsto\sf{216=}\dfrac{4x\times3x}{2}$

$\mapsto\sf{216=}\dfrac{12x^2}{2}$

$\mapsto\sf{216\times2=12x^2}$

$\mapsto\sf{432=12x^2}$

$\mapsto\sf\dfrac{\cancel{432}^{36}}{\cancel{12}^1}=x^2$

$\mapsto\sf{x^2=36}$

$\mapsto\sf{x=\sqrt{6\times6}}$

$\mapsto\sf{x=6}$

Thus,the diagonals of the rhombus are :

$\sf\blue\to{Diagonal_1=4\times6=24}$

And, $\sf\blue\to{Diagonal_2=3\times6=18}$

_________________

Let's verify our diagonals !

$\star{\text{Area of rhombus=}}\dfrac{pq}{2}$

$\leadsto\sf{216}=\dfrac{24\times18}{2}$

$\leadsto\sf{216}=\dfrac{\cancel{432}^{216}}{\cancel{2}^1}$

$\leadsto\sf{216=216}$

Hence,L.H.S. = R.H.S.

Thus,the diagonals we found are correct.

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Answer 2

Explanation:

As we have to find length of both diagonals and diagonals are given in ratio of 4:3 .°. first we have to suppose first diagonal as 4x and second diagonal as 3x. Then by putting values of diagonals and area in formula of rhombus i.e. A= (D1*D2)/2 we will find value of x. (Additional: just verify value of x by putting it value in the equation which is formed by using formula of rhombus. )then finally we will find value of diagonals. To find 1 Digonal we have to multiply x with 4 and to find 2 diagonal we have to multiply x with 3.

☄Now Let's do it :)

Question:

Find the diagonals of a rhombus whose area is 216 metre square and the diagonals are in the ratio 4 is to 3.

To find:

• both diagonals of rhombus

Given:

• Area of rhombus = 216 m
• Diagonals in ratio = 4:3

Let:

• Digonal 1= 4x
• Digonal 2 = 3x

Answer :

We know:

$\bigstar\boxed{\rm \: Area \: of \: rhombus = \dfrac{digonal_1 \times digonal_2}{2} }$

By using this formula we can find value of x.

So let's solve!

put value of Area and both diagonals which we have supposed.

$:\implies \tt \: 216 = \frac{4x \times 3x}{2}$

$:\implies \tt216 \times 2 = 4x \times 3x$

$:\implies \tt432 = 12x^2$

$:\implies \tt \: {x}^{2} = \frac{432}{12}$

$:\implies \tt \: {x}^{2} = \cancel{ \frac{432}{12} }$

$:\implies \tt \: {x}^{2} = 36$

$:\implies \tt \: x = \sqrt{36}$

$:\implies \tt \: x = \sqrt{6 \times 6}$

$:\implies \star \boxed{ \tt \: x = 6 } \star$

Before finding values of both diagonals,Let's Verify value of x.

verification:

$:\implies \tt \: 216 = \frac{4x \times 3x}{2}$

put value of x in this equation

$:\implies \tt \: 216 = \frac{4 \times 6 \times 3 \times 6}{2}$

$:\implies \tt \: 216 = \frac{24 \times 18}{2}$

$:\implies \tt \: 216 = \frac{ 432}{2}$

$:\implies \tt \: 216 = \cancel{ \frac{ 432}{2} }$

$:\implies \star \boxed{ \tt \: 216 = 216} \star$

$\large\dag \bigg(\rm LHS=RHS\bigg)\dag$

☆ Hence Verified ☆

Finally Let's find length of both diagonals.

Put value of x in digonal 1

• Digonal 1 =4x
• Digonal 1= 4×6m
• Digonal 1 = 24m

Put value of x in digonal 2

• Digonal 2 =3x
• Digonal 2= 3×6m
• Digonal 2= 18m

And all we are done! ✔

:D