A rectangle of area 144cm.square has its length equal to x cm. Write down its breadth in terms of x. Given that its perimeter is 52cm, write down an equation in x and solve it to determine the dimensions of rectangle.
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A rectangle of area 144cm.square has its length equal to x cm. Write down its breadth in terms of x. Given that its perimeter is 52cm, write down an equation in x and solve it to determine the dimensions of rectangle.
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Step-by-step 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
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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 .
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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
Solution :
Given that:
Perimeter of rectangle = 44 cm
Area of rectangle = 105 cm2
Length of rectangle = x cm.
Now, perimeter of rectangle = 2 (length +
breadth) = 44
=> 2 (x + breadth) = 44
→ x + breadth = 22
→ breadth of the rectangle = 22 - x Again, area of rectangle = 105 cm2
length x breadth = 105 ⇒ xx (22-x) = 105
→ 22x - x2 = 105
→ x2 - 22x + 105 = 0
⇒ x2 - 15x - 7x + 105 = 0
(x-15)(x-7)= 0
⇒ x = 15 or 7
When x = 15, breadth of the rectangle =
22 x 22 - 15 = 7 cm
and when x = 7, breadth of the rectangle
= 22 - x = 22 - 7 = 15 cm
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