Question

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

Answer 1

Answer:

area = length×breadth

Step-by-step explanation:

daigonol =√l²+b²

solve the both equations you would get the answer

hope it helps you

Answer 2

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.