Respuesta :
ANSWER:
The length and breadth of the rectangle are 18 m and 12 m.
SOLUTION:
Let the length and breadth of a rectangle be "l" and "b"
Given,length and breadth of the rectangle are in ratio 3 : 2
Then, length : breadth :: 3 : 2
[tex]\begin{array}{l}{\frac{l}{b}=\frac{3}{2}} \\\\ {l=\frac{3 b}{2}}\end{array}[/tex] -- eqn 1
After changing the length and breadth by 1 meter on both sides, length and breadth becomes L+2 and b+2
Now, the ratio of length to breadth is 10 : 7
Length : breadth :: 10 : 7
[tex]\frac{l+2}{b+2}=\frac{10}{7}[/tex]
[tex](l +2 ) \times 7 = 10 \times ( b + 2)[/tex]
7l + 14 = 10b + 20
10b – 7l + 20 -14 = 0
10b – 7l + 6 =0 -- eqn (2)
Now, substitute “l” value in (2)
[tex]10 b-7\left(\frac{3 b}{2}\right)+6=0[/tex]
[tex]10 b-\frac{21 b}{2}+6=0[/tex]
20b – 21b + 12 = 0
-b + 12 = 0
b = 12.
Substitute b value in (2)
10(12) – 7l + 6 = 0
120 + 6 = 7l
7l = 126
l = 18
hence, the length and breadth of the rectangle are 18 m and 12 m.
