Question

The area of rectangle is 600m ² and its
perimeter 100m - find its length and breadth​

Answer 1

hope this answer will be helpful ^_^

Answer 2

$\huge\mathtt{SOLUTION:-}$

$\sf\underline{\blue{\:\:\: Given:-\:\:\:}}$

Area if rectangle=600sq.m

Perimeter of rectangle=100m

$\sf\underline{\pink{\:\:\: To\:Find:-\:\:\:}}$

length and breadth of rectangle

Now

$\sf {\red{A.T.Q}}$

$\boxed{\sf{Area\:of\: rectangle=length\times breadth}}$

$\boxed{\sf{Perimeter\:of\: rectangle=2(l+b)}}$

• Let length be x and breadth be y

$\sf perimeter=2(l+b)\\ \\ \sf\implies 100=2(x+y)\\ \\ \sf\implies \cancel{\dfrac{100}{2}}=x+y\\ \\ \sf\implies 50=x+y\\ \\ \sf\implies x=50-y$

• The value of x is 50-y

• and y=y

$\sf\blue{Now\:Area\:of\: rectangle}$

$\sf\implies Area= y\times 50-y\\ \\ \sf\implies 600=50y-y{}^{2}\\ \\ \sf\implies y{}^{2}-50y-600=0\\ \\ \sf\implies y{}^{2}-(60-10)y-600=0\\ \\ \sf\implies y{}^{2}-60y+10y-600=0\\ \\ \sf\implies y(y-60)+10(y-60)=0\\ \\ \sf\implies (y-60)(y+10)=0$

• Y-60=0

• y=60

• The value of y is 60

Now The breadth of rectangle=60

length=50-60 =-10

or 10 because sides can't be negative

$\huge\text{\blue{Proof:-}}$

$\sf\implies Area=l\times b\\ \\ \sf\:\:l=10\:\:\:\:b=60\\ \\ \sf\implies 600=10\times 60\\ \\ \sf\implies 600=600\\ \\ \sf\:\:\:L.H.S=R.H.S\:$

$\boxed{\sf{Length\:of\: rectangle=10m\:\: breadth=60m}}$