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abhi569
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Correct question : the width of a rectangle is half of the length. The area is 25 square meters. What is the perimeter ?





[tex] \bold{ \: solution : - }[/tex]


Let the Length of the rectangle be 2x m and width be half of the length that is ( 2x ÷ 2 ) = x m



We know, Area of Rectangle = length × width

Applying formula,



=> 25 = 2x × x

=> 25 = 2x²

[tex] = > \frac{25}{2} = {x}^{2} [/tex]

=> 12.5 = x²

=> ±√12.5 = x


Dimensions can't be negative, taking positive value,




Therefore,
Breadth = x = √12.5 m
Length = 2x = 2√12.5 m




We know, perimeter of Rectangle = 2( Length + Breadth)




Then,

Perimeter = 2( 2√12.5 + √12.5 ) m

Perimeter = 2( 3√12.5 ) m

Perimeter = 6√12.5 m





Hence, perimeter of the rectangle is 6√12.5 m
onyebuchinnaji

The perimeter of the rectangle is 15√2

The given parameters;

length of the rectangle, L = [tex]\frac{W}{2}[/tex]

the area of the rectangle, A = 25 m²

To find:

  • the perimeter of the rectangle

The area of the rectangle is calculated as;

[tex]A = LW\\\\L = \frac{W}{2} \\\\W = 2L\\\\then, A = L \times 2L\\\\A = 2L^2\\\\L^2 = \frac{A}{2} \\\\L^2 = \frac{25}{2} \\\\L = \frac{\sqrt{25} }{\sqrt{2} } = \frac{5}{\sqrt{2} }[/tex]

The perimeter of the rectangle is calculated as follows;

[tex]P = 2(L + W)\\\\[/tex]

[tex]P = 2(L + 2L)\\\\P = 2 (3L)\\\\P = 6L\\\\P = 6\times \frac{5}{\sqrt{2} } = \frac{30}{\sqrt{2} } \times \frac{\sqrt{2} }{\sqrt{2} } = 15\sqrt{2}[/tex]

Thus, the perimeter of the rectangle is 15√2

Learn more here: https://brainly.com/question/18869010