Answer:
x = 4 cm
Step-by-step explanation:
The area of an rectangle is the product of its length and its breadth.
From the diagram, the length = 13 + x and the breadth = 7 + x. Therefore:
Area of the rectangle = length × breadth = (13+x)(7+x)
But the area = 187 cm,
⇒ 187 = (13+x)(7+x)
187 = x² + 20x + 91
Subtracting 187 from both sides
x² + 20x + 91 - 187 = 187 -187
x² + 20x - 96 = 0
x² + 24x - 4x - 96 = 0
x(x + 24) - 4(x + 24) = 0
(x - 4)(x + 24) = 0
x - 4 = 0 or x + 24 = 0
x = 4 or x = -24
Since x cannot be negative therefore, x = 4 cm
Length = 13 + 4 = 17 cm
Breadth = 7 + 4 = 11 cm
