Question

Find the possible Length and Breadth of the rectangle, perimeter and the Length of the diagonal...

(diagonal has 2 values in root)

Area = 25a² - 35a + 12 ​

Answer 1

✰Solution :

$\:$

☞︎︎︎ Given :

$\:$

• Area = 25a² - 35a + 12

$\:$

★ We know ,

$\:$

➪ Area = Lenghth + breadth

$\:$

★ Area = 25a² - 35a + 12

$\:$

• Splitting The Middle Term :

$\:$

= 25a² - 35a + 12

➪ 25a² - 20a - 15a + 12

➪ 5a(5a - 4) - 3(5a - 4)

= (5a - 3)(5a - 4)

= L × B

$\:$

☞︎︎︎ We have :

$\:$

• Length = 5a - 3

$\:$

• Breadth = 5a - 4

$\:$

✰ Perimeter = 2(lenght + breadth)

$\:$

➪ 2(5a - 3 + 5a - 4)

➪ 2(10a - 7)

➪ 2(10a) - 2(7)

➪ 20a - 14

$\:$

∴ perimeter = 20a - 14

$\:$

• Finding Diagonal :

$\:$

☞︎︎︎ we get right angel triangle by half of rectangle (diagonal)

$\:$

• Pythagoras Theorem :

$\:$

✰ H² = B² + P²

$\:$

• H = To find (diagonal)

• B = 5a - 3

• P = 5a - 4

$\:$

➪ H² = (5a - 3)² + (5a - 4)²

➪ H² = 25a² - 9 + 25a² - 16

➪ H² = 50a² - 25

$\:$

$\large \boxed{\therefore \rm \: diagonal = \sqrt{50 {a}^{2} - 25} }$

Answer 2

Step-by-step explanation:

✰Solution :

\:

☞︎︎︎ Given :

\:

Area = 25a² - 35a + 12

\:

★ We know ,

\:

➪ Area = Lenghth + breadth

\:

★ Area = 25a² - 35a + 12

\:

Splitting The Middle Term :

\:

= 25a² - 35a + 12

➪ 25a² - 20a - 15a + 12

➪ 5a(5a - 4) - 3(5a - 4)

= (5a - 3)(5a - 4)

= L × B

\:

☞︎︎︎ We have :

\:

Length = 5a - 3

\:

Breadth = 5a - 4

\:

✰ Perimeter = 2(lenght + breadth)

\:

➪ 2(5a - 3 + 5a - 4)

➪ 2(10a - 7)

➪ 2(10a) - 2(7)

➪ 20a - 14

\:

∴ perimeter = 20a - 14

\:

Finding Diagonal :

\:

☞︎︎︎ we get right angel triangle by half of rectangle (diagonal)

\:

Pythagoras Theorem :

\:

✰ H² = B² + P²

\:

H = To find (diagonal)

B = 5a - 3

P = 5a - 4

\:

➪ H² = (5a - 3)² + (5a - 4)²

➪ H² = 25a² - 9 + 25a² - 16

➪ H² = 50a² - 25

\:

\large \boxed{\therefore \rm \: diagonal = \sqrt{50 {a}^{2} - 25} }

∴diagonal=

50a

2

−25