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Mrs. Clarkson designed a rectangular garden with a length of 15 meters and a width of 8 meters she plans to build a walkway through the garden from one corner to the next What measure is closest to the length of the diagonal walkway A. 8 meters B. 11 meters C. 17 meters D. 23 meters

Respuesta :

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The Pythagorean Theorem states that if you have two legs of a triangle a and b, the formula for finding the hypotenuse, c, is a^2 + b^2 = c^2. 

The two legs, the length and the width, make a triangle with the diagonal of the rectangle. Therefore:

(15m)^2 + (8m)^2 = c^2

225 m^2 + 64 m^2 = c^2

289 m^2 = c^2

c = 17 m

Answer:

The length of the diagonal walkway is 17 meters (option c)

Step-by-step explanation:

Hi, having a rectangular area is equal to having two triangles with a common side, the hypotenuse.

In this case, the hypotenuse is also the diagonal length between the opposite corners of the garden.

We have to apply the Pythagorean Theorem: c²= a²+b²

Where c is the hypotenuse, and the other variables are the legs of the triangle, in this case, the width and length of the garden (15 and 8)

So, replacing with the values given:

c²= a²+b²

c²= 15²+8²

c²= 225 +64

c²= 289

c= √289

c = 17

The length of the diagonal walkway is 17 meters (option c)

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