Question

when an iron rod of length 56 cm is bent in to a rectangle and the distance between its opposite vertices is 20 cm. find the length and breadth of the rectangle​

Answer 1

Answer:

length of rod is 56cm therefore perimeter of rectangle is 56cm

:. 2(l+b)= 56cm

l+b= 28cm

l=28-b

Distance between its opposite vertices is 20cm

therefore length of diagnal = 28cm

According to Pythagoras theorem-

(20)²=l²+b²

400= (28-b)² +b²

400= 784+b² -56b +b²

0=2b²-56b+784-400

0=2b²-56b+384

0= b²-28b+192

0=b²-24b-4b+192

0=b(b-24)-4(b-24)

0=(b-4)(b-24)

b=4 or b=24

If b=4cm,

l=28-b=28-4=24cm

If b=24cm,

l=28-b=28-24=4cm