Question

The length of a rod is 56 centimetres. It is bent into a rectangle.
(a) What is the sum of length and breadth of the rectangle?
(b) If the length of diagonal of this rectangle is 20 centimetres, then find the length and
breadth of this rectangle?​

Answer 1

(a) Perimeter is 56 cm

( l + b )× 2 = perimeter

l + b = Perimeter ÷ 2

l + b= 56÷2=28 cm

Answer is 28 cm

Answer 2

Answer:

Step-by-step explanation:

length of rod=l=56cm

Now we know that

2(l+b)=56

so

l+b=28  ...........(1)

which is (a)

for b

if we take the diagonal as the hypotenuse of a right angled triangle and the length and breadth of the rectangle as the other two sides

l^2+b^2=diagonal^2 ..........(2)

from (1)

l=28-b

Sub in (2)

(28-b)^2 + b^2=diagonal^2

784 - 56b +b^2+b^2=(20)^2

384-56b+2b^2=0

192-28b+b^2=0

D=b^2-4ac=784-768=16

b=(-b(+/-)rootD)/2a=(28(+/-)16)/2=

b=22 or b=6

Now take these values as two case and substitute each of the values in (1) and you will get your answer

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