# Linear Equations-algebraic method-eleventh grade-5

### From Homeworkwiki

**The length of a hall is twice its breadth. If both the length and the breadth be increased by 2 meters,**

**the area of the hall will increase by 52 sq. meters. Find the area of the hall.**

**Solution:** Let the breadth be x meters. Then length is 2x meters.

Area = l X b

= (2x)x = 2x^{2} sq. meters.

(x + 2)(2x + 2) = 2x^{2} + 52

i.e. 2x^{2} + 6x + 4 = 2x^{2} + 52

Therefore, 6x + 4 = 52

i.e. 6x = 52 – 4 = 48

Therefore, x = 48 / 6 = 8

Area = 2x^{2} = 2 (8)^{2} = 128 sq. meters.