A rectangular pool has area 2x² + 7x + 3 square hastas. If its width is 2x + 1 hastas find its length Class 9

A rectangular pool has area 2x² + 7x + 3 square hastas. If its width is 2x + 1 hastas find its length Class 9

Question 1.

A rectangular pool has area 2x² + 7x + 3 square hastas. If its width is 2x + 1 hastas, find its length. Hasta was a unit used to measure length. Class 9

Solution:

Given : Area = 2x² + 7x + 3 square hastas,

Width = 2x + 1 hastas

We know that,

Area = Length × Width

Length = $\frac{\text { Area }}{\text { Width }}$

∴ Length = $\frac{2 x^2+7 x+3}{2 x+1}$

2x² + 7x + 3 = $2\left(x^2+\frac{7}{2} x+\frac{3}{2}\right)$

Since $\frac{1}{2}+3=\frac{7}{2}$ and $\frac{1}{2} \times 3=\frac{3}{2}$, the numbers are $\frac{1}{2}$ and 3.

∴ 2x² + 7x + 3 = 2 (x + $\frac{1}{2}$)(x + 3)

= (2x + 1)(x + 3)

∴ Length = $\frac{(2 x+1)(x+3)}{2 x+1}$

= (x + 3) hastas

..[Cancelling the common factor (2x + 1)]

∴ The length of the rectangular pool is (x + 3) hastas.