Question

21. The outside dimensions of a bordered table cloth are
72 cm and 108 cm. If the area of the table cloth
excluding the border is 6400 cm², how wide is the
border.​

Answer 1

Given,

The outside dimensions of the table cloth = 72cm and 108 cm

The area of the table cloth excluding the borders is 6400 cm².

To find,

The width of the borders.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the width of border = x cm

Internal length = 108- (2×x) = 108-2x cm

Internal width = 72 - (2×x) = 72-2x cm

Internal area = (108-2x) × (72-2x) = (7776-144x-216x+4x²) cm² = (7776-360x+4x²) cm²

According to the data mentioned in the question,

(7776-360x+4x²) = 6400

4x²-360x+7776-6400 = 0

4x²-360x+1376 = 0

(x-4) (x-86) = 0

So,

x = 4

or,

x = 86

Now, we cannot take 86 as the value because it is greater than the width itself.

So, the width of the border = 4 cm

Hence, the width of the border is 4 cm.

Answer 2

Answer:

4 or 86

Step-by-step explanation:

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