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Answers
Explanation:
Answer:-
Dimensions of the rectangle are 18cm [length] and 8cm [breadth] .
Explanation:-
We have :-
→ Area of the rectangle = 144 cm²
→ Length = x cm
→ Perimeter = 52 cm
________________________________
Let the assume that the breadth of the rectangle is 'b' cm.
Area of a rectangle = Length × Breadth
⇒ x × b = 144
⇒ b = 144/x
Hence, breadth in terms of 'x' is 144/x .
________________________________
Now :-
Perimeter of a rectangle :-
= 2( Length + Breadth )
⇒ 2( x + 144/x ) = 52
⇒ 2x + 288/x = 52
⇒ 2x² + 288 = 52x
⇒ 2x² - 52x + 288 = 0
⇒ 2(x² - 26x + 144) = 0
⇒ 2(x² - 8x - 18x + 144) = 0
⇒2[x(x - 8) - 18(x - 8)] = 0
⇒ 2(x - 18)(x - 8) = 0
⇒ x = 18 ; x = 8
Answer:
Explanation:
Answer:-
Dimensions of the rectangle are 18cm [length] and 8cm [breadth] .
Explanation:-
We have :-
→ Area of the rectangle = 144 cm²
→ Length = x cm
→ Perimeter = 52 cm
________________________________
Let the assume that the breadth of the rectangle is 'b' cm.
Area of a rectangle = Length × Breadth
⇒ x × b = 144
⇒ b = 144/x
Hence, breadth in terms of 'x' is 144/x .
________________________________
Now :-
Perimeter of a rectangle :-
= 2( Length + Breadth )
⇒ 2( x + 144/x ) = 52
⇒ 2x + 288/x = 52
⇒ 2x² + 288 = 52x
⇒ 2x² - 52x + 288 = 0
⇒ 2(x² - 26x + 144) = 0
⇒ 2(x² - 8x - 18x + 144) = 0
⇒2[x(x - 8) - 18(x - 8)] = 0
⇒ 2(x - 18)(x - 8) = 0
⇒ x = 18 ; x = 8