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A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section.
What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines?

A 15meter by 23meter garden is divided into two sections Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectan class=

Respuesta :

Edufirst
1) The square section

The side length of the square is 15m.

You can use Pythagora's theorem to find the length of the diagonal:

Diagonal ^2 = (15m)^2 + (15m^2) = 450 m^2

=> Diagonal = √(450m^2) = 21.21m

2)  The small rectangle section

The sides of this rectangle are 23 - 15 = 8 m and 15 m

Now use the Pythagora's theorem:

diagonal^2 = (8m)^2 + (15m)^2 = 289 m^2 =>

diagonal = √(289m^2) = 17 m

3) Then the sum of the lengths of the diagonals of the two sections  is 17m + 21.21 m = 38.21

Answer: 38.21 m

The approximate sum of the lengths of the two sidewalks, shown as dotted lines is 38.21m.

Given that,

Total Length of the garden = 23m

The side length of the square section = 15m

The side length small rectangle section =  23m - 15m = 8 m

We have to find,

The approximate sum of the lengths of the two sidewalks, shown as dotted lines.

According to the question,

The square section,

The side length of the square is 15m.

By using Pythagoras theorem the length of the diagonal:

[tex]( Diagonal )^{2}[/tex] [tex]= (15m)^{2} + (15m)^{2}[/tex] [tex]= 450m^{2}[/tex]  

Diagonal = [tex]\sqrt{450m^{2} }[/tex] = 21.21m

The small rectangle section,

The sides of small rectangle are =  23m - 15m = 8 m  

Now, By using the Pythagoras theorem:

[tex](Diagonal)^{2} = (8m^{2} ) + (15^{2}m) = 289m^{2}[/tex]

Diagonal = [tex]\sqrt{289m^{2} }[/tex] = 17 m

The sum of the lengths of the diagonals of the two sections is,

=  17m + 21.21 m = 38.21m

Hence, The approximate sum of the lengths of the two sidewalks, shown as dotted lines is 38.21m.

For the more information about Pythagoras Theorem click the link given below.

https://brainly.com/question/20213211

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