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Solution


Q.

In the picture given, one can see a rectangular in-ground swimming pool. There is a concrete sidewalk of width x metres around the pool. The outside edges of the sidewalk measure 7 m and 12 m. The area of the pool is 36 m².

Answer the following:

 

(i) Based on the information above, form a quadratic equation in terms of x.
1 0  
2 1  
3 2  
4 3  

Ans.

(1)

Let x be the uniform width of the sidewalk. Then the pool’s inside dimensions are:

Length of pool = 12 − 2x  metres

Breadth of pool = 7 − 2x  metres

Given: Area of pool = 36 m²

Therefore, (12 − 2x)(7 − 2x) = 36

⇒ 84 − 14x − 24x + 4x² = 36

⇒ 4x² − 38x + 48 = 0  ⇒  2x² − 19x + 24 = 0

This is the required quadratic equation in x.