Mathematics High School

Lucas has a 39-foot-long rope. He uses all the rope to outline this T-shape in his backyard. All the angles in the figure are right angles. (Work out and answer number 13 and number 14, please.)

Lucas Has A 39-foot-long Rope. He Uses All The Rope To Outline This T-shape In His Backyard. All The

Answers

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The area of a shape is the amount of space it can occupy, while the perimeter is the sum of its sides.

The value of x is 7.5 ftThe area of the shape is 57 square feet

Given that:

[tex]P = 39[/tex] --- the perimeter of the shape

The value of x

The perimeter is the sum of all sides.

So, we have:

[tex]P = x + x + 3.5 + 3.5 + 3 + 3 + 9 + (9 - 3.5 - 3.5)[/tex]

Substitute 39 for P

[tex]x + x + 3.5 + 3.5 + 3 + 3 + 9 + (9 - 3.5 - 3.5) = 39[/tex]

[tex]2x + 24 = 39[/tex]

Collect like terms

[tex]2x = -24 + 39[/tex]

[tex]2x = 15[/tex]

Divide through by 2

[tex]x = 7.5[/tex]

The area of the shape

The shape can be divided into two rectangles

A 9ft by 3ft rectangleA (9 - 3.5 - 3.5)ft by x ft rectangle

So, the area of the shape is:

[tex]Area = 9ft \times 3ft + (9 - 3.5 - 3.5)ft \times x ft[/tex]

[tex]Area = 27ft^2 + 2ft \times x ft[/tex]

Substitute [tex]x = 7.5[/tex]

[tex]Area = 27ft^2 + 2ft \times 15 ft[/tex]

[tex]Area = 27ft^2 + 30 ft^2[/tex]

[tex]Area = 57 ft^2[/tex]

Hence, the area of the shape is 57 square feet.

Read more about areas and perimeters at:

https://brainly.com/question/16103242

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Answers

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Step-by-step explanation:

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