Answer:
length : 8 m
width : 13/2 = 6.5 m
Step-by-step explanation:
area of rectangle = l(ength)×w(idth) = 52
l = 2w - 5
=> (2w - 5)×w = 52
=> 2w² -5w - 52 = 0
we know, when transforming this quadratic equation into a multiplication of two expressions of w, that we need to have 2w and w (to make 2w²), and then which 2 numbers multiply to 52 and add to -5 (when one is multiplied by 2 due to 2w) : -13 and 4
=> (2w - 13)×(w + 4) = 0
=> 2 solutions for w :
2w-13 = 0
2w = 13, w = 13/2
w+4 = 0, w = -4
negative values for a side length of a shape do not make sense, so the only usable solution is w = 13/2
=> l = 2w - 5 = 13 - 5 = 8
