Question

1. The length of a swimming pool is 8m longer than its width and the area is 105m2.

Answer 1

$width : w \\ length : \ l = w + 8 \\ A = 105 \ m^2 \\ \\A= w \cdot l \\ \\w(w+l)=105 \\ \\w^2+w = 105 \\ \\w^2+w-105 =0 \\ \\(w+15)(w-7)=0 \\ \\w+15 =0 \ \ or \ \ w-7 = 0 \\ \\w = -15 \ \ or \ \ w=7 \\ \\ width \ cant \ be \ negative, \ so \\ \\ w = 7 \ and \ l = w+8 = 7 +8 =15 \\ \\chek : \\ \\ A=w\cdot l \\ \\A=7\cdot 15=105 \ m^2$