Question

The area and diagonal of a rectangle are 60cm^2 and 13cm respectively. Find the length of the rectangle.

Answer 1

The length of the rectangle is "5 cm or 12 cm".

Step-by-step explanation:

Let length of the rectangle = l and breadth of the rectangle = b

∴ l × b = 60  

⇒ l =  $\dfrac{b}{60}$                                ... (1)                      

and  $\sqrt{l^{2} + b^{2} }$ = 13              ... (2)

[since, diagonal = $\sqrt{l^{2} + b^{2} }$]

Squaring (2) in both sides, we get

$l^{2} + b^{2}$ = 169                                                               ... (3)

From (1) and (3), we get

$\dfrac{3600}{b^{2}} + b^{2} = 169$

⇒ $b^{4} - 169b^{2} + 3600 = 0$    

⇒ $b^{4} - 169b^{2} + 3600 = 0$    

Put  $b^{2}$ = x

$x^{2} - 169x+ 3600 = 0$    

⇒  $x^{2} - 144x -25x + 3600 = 0$         

⇒(x -144)(x -25) = 0

∴ x = 144 or 25

⇒ x = 144 or 25

∴ b = ± 12 or ± 5

b = 12 cm or 5 cm (Since, length never be negative]

Putting the value of b in (1), we get

l × 12 = 60  or l × 5 = 60

l = 5 cm or 12 cm

Hence, the length of the rectangle is 5 cm or 12 cm.