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Alenkasestr [34]
3 years ago
11

A teacher runs a total of 48 city blocks in a rectangular pattern. If the width of the run is 3x and the length of the run is 5x

+ 4, what is the perimeter of the path the teacher runs? all you have to do is a equation don't solve it :)
Mathematics
1 answer:
Ghella [55]3 years ago
6 0

Answer:

P = 16x + 8

Step-by-step explanation:

Perimeter of a rectangle

= 2(L + W)

Given

L = 5x + 4 and

W = 3x

Therefore

Perimeter = 2(5x + 4 + 3x)

Rearrange the expression

P = 2(5x + 3x + 4)

P = 2(8x + 4)

Now expand the bracket

P = 2 x 8x + 2 x 4

P = 16x + 8

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\huge \boxed{\mathbb{QUESTION} \downarrow}

  • Find x.

\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}

To solve these type of problems you need to use the pythagoras theorem ⇨ Hypotenuse² = Base² + Altitude².

Here,

  • Altitude = 1.6 cm.
  • Base = 1.2 cm
  • Hypotenuse = x

Now, let's solve for x.

Hypotenuse² = Base² + Altitude²

x² = (1.2)² + (1.6)²

x² = 1.44 + 2.56

x² = 4

x = √4

x = <em><u>2</u></em><em><u>.</u></em>

  • So, the value of x is <em><u>2</u><u> </u><u>cm.</u></em>

<h3><u>NOTE</u><u> </u><u>:</u><u>-</u></h3>
  • Pythagoras theorem can be used only in the cases of right-angled triangles. Here, it's given that the triangle is right angled so we can use this theorem.
  • To solve the squares if decimals, take them as whole numbers & then just add the decimal points. For example, ⇨ for (1.2)², take it as 12² , then multiply 12 by 12, you'll get 144. Now, add the decimal place accordingly ⇨ 1.44 . So, (1.2)² = 1.44.
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