In the given diagram, the area of the shaded region is 57 m 2 . Form an equation in x and solve it to find the possible value of x.

Given,

Area of the shaded region = 57 m²

From the figure,

Length of the outer rectangle = 12 m

Breadth of the outer rectangle = 10 m

Area of the outer rectangle = 12 × 10 = 120 m²

Length of the inner (unshaded) rectangle = (12 − x) m

Breadth of the inner (unshaded) rectangle = (10 − x) m

Area of the inner rectangle = (12 − x)(10 − x) m²

From the figure,

Area of shaded region = Area of outer rectangle − Area of inner rectangle

⇒ 12 × 10 − (12 − x)(10 − x) = 57

⇒ 120 − (120 − 12x − 10x + x²) = 57

⇒ 120 − 120 + 22x − x² = 57

⇒ 22x − x² = 57

⇒ x² − 22x + 57 = 0

⇒ x² − 19x − 3x + 57 = 0

⇒ x(x − 19) − 3(x − 19) = 0

⇒ (x − 19)(x − 3) = 0

[Using zero product rule]

⇒ (x − 19) = 0 or (x − 3) = 0

⇒ x = 19 or x = 3

Since, the breadth of the rectangle is 10 m, the width x cannot be 19 m.

∴ x = 3 m.

Hence, the possible value of x = 3 m.