What are the side lengths of a rectangle if the area is 40 inΒ² and the perimeter is 48 in?
Answer (2)
a , b β t h e s i d e l e n g t h s o f a rec t an g l e a β
b = 40 [ i n 2 ] β§ 2 β
( a + b ) = 48 [ in ] a + b = 24 β a = 24 β b β ab = ( 24 β b ) b = 24 b β b 2 ab = 40 β 24 b β b 2 = 40 β β b 2 + 24 b β 40 = 0 / β
( β 1 ) b 2 β 24 b + 40 = 0 β Ξ = ( β 24 ) 2 β 4 β
40 = 576 β 160 = 416 = 16 β
26
Ξ β = 4 26 β β b 1 β = 2 24 β 4 26 β β = 12 β 2 26 β β a 1 β = 12 + 2 26 β . b 2 β = 2 24 + 4 26 β β = 12 + 2 26 β β a 2 β = 12 β 2 26 β
The side lengths of the rectangle are approximately 7.3 in and 5.5 in based on the area of 40 inΒ² and the perimeter of 48 in. We used the area and perimeter formulas to derive a quadratic equation that helped us find the side lengths. After solving, we found the two potential dimension pairs from the quadratic results.
;
