Find the possible Length and Breadth of the rectangle, perimeter and t

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

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»

✰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

$\:$

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