Mathematics Question and Solution
Calculating Area Green.
Let z be the width of the ascribed rectangle.
Let y be the length of the ascribed rectangle.
½(az) = 22
a = 44/z cm.
½(by) = 48
b = 96/y cm.
c = y-44/z
c = (yz-44)/z cm.
d = z-96/y
d = (zy-96)/y cm.
It implies;
½((yz-44)/z)((zy-96)/y) = 12
24zy = (yz-44)(zy-96)
24zy = (zy)²-140zy+4224
(zy)²-164zy+4224 = 0
Let zy = e.
e²-164e+4224 = 0
Calculating e.
(e-82)² = -4224+(-82)²
(e-82)² = -4224+6724
(e-82)² = 2500
e = 82±√(2500)
e = 82±50
Therefore;
e ≠ 82-50 = 32
e = 82+50
e = 132
Recall.
e = zy (area of the ascribed rectangle)
It implies,
zy = 132 cm²
Therefore, green area is;
zy-22-48-12
= 132-82
= 50 cm²
