Question

14. The area and the diagonal of a rectangle are 60 cm2 and 13 cm. Find the length.​

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

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

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

Squaring (1) in both sides, we get

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

From (1) and (3), we get

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

⇒  $b^{4} - 169b^{2} + 3600 = 0$   

Put  $b^{2}$ = x

$x^{2} - 169x + 3600 = 0$     

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

⇒ 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 = 5 cm or 12 cm

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