If the perimeter of rectangle is 52metere and area is 160m² thae leng

1.	If the perimeter of rectangle is 52metere and area is 160m² thae lenghth of rectangle is
Answer» GIVEN :- AREA of the RECTANGLE = 160 m² Perimeter of the rectangle = 52 m To Find :- Length of the rectangle Solution :- Perimeter of the rectangle :- $:\implies\sf{Perimeter = 2(l+b)}$ $:\implies\sf{52 = 2(l+b)}$ $:\implies\sf{52/2 = (l+b)}$ $:\implies\sf{26 = (l+b)}$ $:\implies\sf{b=26-l}...(1)$ Area of the rectangle :- $:\implies\sf{Area = l \times b}$ $:\implies\sf{160 = l \times (26-l)}$ $:\implies\sf{160 = 26l-l^2}$ $:\implies\sf{ 26l-l^2-160=0}$ $:\implies\sf{ -l^2+26l-160=0}$ $:\implies\sf{ l^2-26l+160=0}$ $:\implies\sf{ l^2-10l-16l+160=0}$ $:\implies\sf{ l(l-10)-16(l-10)=0}$ $:\implies\sf{ (l-10)(l-16)=0}$ $:\implies\sf{ (l=16)\:or\:(l=10)}$ So, Length of the rectangle = 16 m Breadth of the rectangle = 10 m To check ↓ ➥ Area of the rectangle = l × b ➥ Area = 16 × 10 ➥ Area = 160 m² Hence VERIFIED!