Question

There is a rectangular field of area 48cm.sq sum of its diagonal and length is 3 times of its breadth.find the length and the breadth of the recatangle.

Answer 1

Let :
Length = l
Breadth = b
Diagonal (d) = ( l^2 + b^2) ^ 1/2 - By pythagoras' theorem

Area =l x b
48 = l x b
48/l = b


d + l = 3(b) - Given
( l^2 + b^2) ^ 1/2 + l = 3( 48 /l)
( l^2 + b^2) ^ 1/2 = 144/l - l

Squaring both sides

l^2 + b^2 = 20736/l^2 + l^2 - 288
(48/l)^2 = 20736/l^2 - 288
2304/l^2 - 20736/l^2 = - 288
288 = 18432/l^2
l^2 = 64
Therefore l= 8 cm ( - ve neglected)

b= 48/l
= 48/8
= 6 cm

Answer 2

Please see the attachment