Question

the area of rectangle is 4: 5 and the perimeter of the rectangle is 108 find its diagonals and its area ​

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

$\tt Given \begin{cases} \sf{Area \: of \: rectangle \: is \: 4 :5} \\ \sf{Perimeter \: of \: rectangle \: is \: 108}\end{cases}$

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To Find :

We have to find Area and Diagonals of rectangle

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Solution :

Let 5x be Length (L)

Let 4x be Breadth (B)

We know that,

$\Large{\star{\underline{\boxed{\sf{Perimeter = 2(L + B)}}}}}$

108 = 2(5x + 4x)

108/2 = 9x

54 = 9x

54/9 = x

6 = x

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∴ Breadth = 4(6) = 24 cm

∴ Length = 5(6) = 30 cm

$\large{\star{\underline{\boxed{\sf{Breadth = 24 \: cm}}}}}$

$\large{\star{\underline{\boxed{\sf{Length = 30 \: cm}}}}}$

$\rule{200}{2}$

Now,

$\Large{\star{\underline{\boxed{\sf{Area = L \times B}}}}}$

Area = 24 * 30

Area = 720 cm²

$\Large{\star{\underline{\boxed{\sf{Area = 720 \: cm^2}}}}}$

$\rule{200}{2}$

$\Large{\underline{\boxed{\sf{Diagonal \: of \: rectangle \: = \: \sqrt{(l^2 + b^2)}}}}}$

Put Values ,

⇒ Diagonal = √((24)² + (30)²)

⇒Diagonal = √(576 + 900)

⇒Diagonal = √1476

⇒Diagonal = 38.4 cm

∴ Diagonal of rectangle is 38.4 cm

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