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A garden has the form of a right triangle. One leg of the triangle is formed by a 2000-ft long sea wall. The hypotenuse of the triangle is 400 ft longer than the other leg. What are the dimensions of the garden?

Respuesta :

MrRoyal

Answer:

[tex]H = 5200[/tex] - Hypotenuse

[tex]S_1 = 2000[/tex] - Leg 1

[tex]S_2 = 4800[/tex] - Leg 2

Step-by-step explanation:

Represent the dimensions as:

[tex]H = Hypotenuse[/tex]

[tex]Other\ Legs = \{S_1,S_2\}[/tex]

So, we have:

[tex]S_1 = 2000[/tex]

[tex]H = 400 + S_2[/tex]

Required

Determine the dimensions

Apply Pythagoras theorem

[tex]H^2 = S_1^2 + S_2^2[/tex]

This gives:

[tex](400 + S_2)^2 = 2000^2 + S_2^2[/tex]

Open bracket

[tex]160000 + 800S_2 + S_2^2 = 4000000 + S_2^2[/tex]

[tex]160000 + 800S_2 = 4000000[/tex]

Collect Like Terms

[tex]800S_2 = 4000000 - 160000[/tex]

[tex]800S_2 = 3840000[/tex]

Solve for S2

[tex]S_2 = \frac{3840000}{800}[/tex]

[tex]S_2 = 4800[/tex]

Recall that:

[tex]H = 400 + S_2[/tex]

[tex]H = 400 + 4800[/tex]

[tex]H = 5200[/tex]

Hence, the dimensions are:

[tex]H = 5200[/tex]

[tex]S_1 = 2000[/tex]

[tex]S_2 = 4800[/tex]

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