Question

find the length of the rectangle whose diagonal is 25 cm and area is 168 cm​

Answer 1

Answer:

So the length of the rectangle is 24 cm and it's breadth is 7 cm.

Step-by-step explanation:

Let the length of the rectangle be x cm and it's breadth be y cm. The length of its diagonal is 25 cm.

=> x^2 + y^2 = 25^2

=> y^2 = 625 - x^2 => y = √(625 - x^2)

Now area of the rectangle = l × b

=> x × √(625 - x^2) = 168. Squaring both sides we get

x^2 × (625 - x^2) = 168^2

=>625x^2 - x^4 = 28224

=> x^4 - 625 x^2 +28224 = 0

=>(x^2 - 576)(x^2 - 49) = 0

=x^2 = 576 or 49 => x = 24 or 7

So the length of the rectangle is 24 cm and it's breadth is 7 cm.