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HERE IS A RECTANGLE ABCD 30CM=WIDTH AND 20CM=LENGTH AND LETTERS ABCD THE LENGH OF THE RECTANGLE IS INCREASED BY 10% AND THE WIDTH OF THE RECTANGLE I INCREASED BY 5%. WHAT IS THE PERCENTAGE INCREASE THE PERIMETER OF THE RECTANGLE?

Respuesta :

semsee45

Answer:

7%

Step-by-step explanation:

Perimeter of a rectangle

P = 2(w + l)

where:

  • P = perimeter
  • w = width
  • l = length

Given:

  • Width of rectangle = 30 cm
  • Length of rectangle = 20 cm

Therefore, the perimeter of the original rectangle is:

⇒ P = 2(30 + 20)

⇒ P = 2(50)

⇒ P = 100 cm

If the width is increased by 5%:

⇒ new width = 30 × 1.05 = 31.5 cm

If the length is increased by 10%:

⇒ new length = 20 × 1.1 = 22 cm

Therefore, the new perimeter will be:

⇒ P = 2(31.5 + 22)

⇒ P = 2(53.5)

⇒ P = 107 cm

Percentage Increase

[tex]\sf PI=\dfrac{final\:value-initial\:value}{initial\:value} \times 100[/tex]

Substitute the values:

[tex]\begin{aligned} \implies \sf Percentage\:increase & = \sf \dfrac{new\:perimeter-original\:perimeter}{original\:perimeter} \times 100\\\\& = \sf \dfrac{107-100}{100} \times 100\\\\& = \sf 7\%\end{aligned}[/tex]

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