Question

A rectangular garage has a perimeter of 46 meters and an area of 130 square meters. What are the dimensions of the garage?

Answer 1

l×b = 130
2(l+b) =46
l+b = 23
b = 23-l
so ,
l×(23-l)= 130
23l-l²=130. => -l²+23l-130= 0
=> -l²+13l+10l-130 = 0
=> -l(l-13) +10(l-13) = 0
(l-13)(10-l)=0
so , length can be l-13=0 => l= 13m
or can be 10-l = 0 => l= 10m
if length is 13m ,
breadth = l×b = 130
13× b = 130 => b= 10m
if length is 10m
breadth = l×b = 10 × b = 130 m
b = 13m
hope this helps

Answer 2

Let the length be l

Let the breadth be b

Therefore ,

Perimeter of Rectangular garage -

2(l+b) = 46m
→ l+b = 23m...............1

Area of Rectangular garage -

lb = 130
→ b = 130/l..................2


putting 2 in 1

l + (130/l) = 23

or, l² + 130 = 23l

or, l² - 23l +130 = 0

or, l² - 13l -10l +130 = 0

or, l(l-13)-10(l-13) = 0

or, (l-10)(l-13)

→ l = 13 or 10

b = 130/13 = 10 (putting value of l in 2)

length of Rectangular garage is 13m and breadth is 10m.
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