Question

a rectangle is 8 km longer than it is wide. find the dimensions of the rectangle if its area is 240 sq-km.

Answer 1

The dimensions of the rectangle are, length is 20 cm and the width is 12 cm.

What is an area?

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Let

The width of the rectangle is x.

As length is 8km longer than than width.

So length = x + 8

The area of the rectangle is 240 sq - km

Since,

   Area of rectangle = length x width

                        240   = (x + 8) x x

                          240 = x^2 + 8x

         x^2 + 8x - 240 = 0

x^2 + 20x - 12x -240 = 0

x(x + 20) - 12(x + 20) = 0

          (x + 20)(x 2 12) = 0

⇒ (x + 20) = 0,     (x - 12) = 0

⇒   x = -20,           x = 12

Since, length is not negative.

So, x = 12

Hence, the width of the rectangle is 12 cm and the length of the rectangle is 12 + 8 = 20 cm.

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