Question

the diagnosis of a rhombus are in the ratio 5:6 if the are is 240 cm square find the length of the diagonals

Answer 1

Answer:

let diagonals be 5x and 6x

Area of rhombus = 1/2 × product of diagonals

According to statement

Step-by-step explanation:

240=1/2X5x X6x

480=30x^2

x^2=16

x=4

so length of diagonals are 20 and 24 cm

Answer 2

$\huge\bold{\mathtt{Question⇒}}$

the diagonals of a rhombus are in the ratio $5:6.$ If the area is $240$ cm², square find the length of the diagonals.

$\huge\bold{\mathtt{Given⇒}}$

• Ratio $= 5:6$

• Area $= 240$ cm²

$\huge\bold{\mathtt{To\:find⇒}}$

The length of the diagonals.

$\huge\bold{\mathtt{Question⇒}}$

Let the diagonals are of $5x$ cm and $6x$ cm respectively.

We know that:

• $\boxed{\tiny\mathtt{Area\:of\:rhombus={\frac{1}{2}}×Product\:of\:two\:diagonals}}$

According to condition,

${{\frac{1}{2}}×5x×6x=240}$

$➳\:{{\frac{1}{2}}×30x=240}$

$➳\:{{\frac{1}{\cancel{2}}}×\cancel{30}x²=240}$

$➳\:15x² = 240$

$➳\:x² = ({\frac{240}{15}})$

$➳\:x² = 16$

$➳\:x ={\sqrt{16}}$

$➳\:x = 4$

$\huge\bold{\mathtt{Hence⇒}}$

$x = 4$

Substituting $x$ with $4.$

• $5x$ cm $= (5×4)$ cm $= 20$ cm

• $6x$ cm $= (6×4)$ cm $= 24$ cm

$\huge\bold{\mathtt{Therefore⇒}}$

The length of its diagonals are $20$ cm and $24$ cm respectively.

$\huge\bold{\mathtt{Not\:sure\:??}}$

$\huge\bold{\mathtt{Verification⇒}}$

${{\frac{1}{2}}×5x×6x=240}$

Putting the length of the diagonals.

$➳\:{{\frac{1}{2}}×20×24=240}$

$➳\:{{\frac{1}{2}}×480=240}$

$➳\:{{\frac{1}{\cancel{2}}}×\cancel{480}=240}$

$➳\:{240=240}$

So, L.H.S $=$ R.H.S.

Hence, verified.

$\huge\bold{\mathtt{Done}}$

• $\large\bold{\mathtt{Hope\:this\:helps\:you.}}$

• $\large\bold{\mathtt{Enjoy\: learning\:!!}}$

• $\large\bold{\mathtt{Have\:a\:nice\:day.}}$