The length of the rectangle is 8 in and the breadth of the rectangle is 5 in
Given:
area of the rectangle, A = 40 in²
perimeter of the rectangle, P = 26 in
To find:
the length of each side of the rectangle
let the length of the rectangle = L
let the breadth of the rectangle, = b
The area is calculated as;
A = Lb
40 = Lb
[tex]L = \frac{40}{b}[/tex] --------- (1)
The perimeter is calculated as;
P = 2( L + b)
P = 2L + 2b
26 = 2L + 2b -------- (2)
Substitute the value of L in (2)
[tex]2L + 2b = 26\\\\2 (\frac{40}{b} ) + 2b = 26\\\\\frac{80}{b} + 2b = 26\\\\multiple \ through \ by \ b\\\\80 + 2b^2 = 26b\\\\2b^2- 26b + 80 = 0\\\\divide \ through \ by \ 2\\\\b^2 - 13b + 40 = 0\\\\factorize \ the \ above \ quadratic \ equation\\\\b^2 - 5b - 8b + 40 = 0\\\\b(b - 5) -8(b - 5) = 0\\\\(b-5)(b-8)=0\\\\b = 5 \ in \ \ or \ \ 8\ in[/tex]
The length is calculated as;
L = 40/b
L = 40/5 = 8 or 40/8 = 5
Since length is always bigger than breadth, then we can conclude that:
the length of the rectangle = 8 in
the breadth of the rectangle = 5 in
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