A rectangular pool has area 2x^2 + 7x + 3 square hastas. If its…

Question 39 of 43intermediate🔧 ApplyShort Answer3 marks

A rectangular pool has area $2x^{2}$ + 7x + 3 square hastas. If its width is 2x + 1 hastas, find its length. Hasta was a unit used to measure length.

Correct Answer

x + 3 hastas

Exercise: END-OF-CHAPTER EXERCISES | Q: 9 | (Page 23)

For More Understanding

Explanation

The area of a rectangle is the product of its length and width. To find the length, the area polynomial must be factored. By splitting the middle term of the quadratic expression for area, we find its dimensions as the factors. One factor matches the given width, leaving the other factor as the length.

Solution Steps

Step 1: Relationship: Area = Length × Width. So, Length = Area ÷ Width.
Step 2: Factorize Area: Factorize $2x^2 + 7x + 3$ by splitting the middle term. Find two numbers that multiply to $2 \times 3 = 6$ and add to $7$ . These are $6$ and $1$ .
Step 3: Split and group: $2x^2 + 7x + 3 = 2x^2 + 6x + x + 3 = 2x(x + 3) + 1(x + 3) = (2x + 1)(x + 3)$ .
Step 4: Determine Length: Since Area = $(2x + 1)(x + 3)$ and Width = $2x + 1$ , the Length = $x + 3$ hastas.

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