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A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 14 feet more than the length of the shortest side. Find the dimensions if the perimeter is 146 feet.

Respuesta :

calculista

Answer:

The dimensions of triangle are 66 ft, 33 ft and 47 ft

Step-by-step explanation:

Let

x -----> the length of one side

y -----> the length of the shortest side

z -----> the length of the third side

we know that

The perimeter of triangle is

[tex]P=x+y+z[/tex]

[tex]P=146\ ft[/tex]

so

[tex]146=x+y+z[/tex] -----> equation A

[tex]x=2y[/tex] -----> equation B

[tex]z=y+14[/tex] ----> equation C

Substitute equation B and C in equation A and solve for y

[tex]146=2y+y+y+14[/tex]

[tex]146=4y+14[/tex]

[tex]4y=146-14[/tex]

[tex]4y=132[/tex]

[tex]y=33\ ft[/tex]

Find the value of x

[tex]x=2(33)=66\ ft[/tex]

Find the value of z

[tex]z=33+14=47\ ft[/tex]

therefore

The dimensions of triangle are 66 ft, 33 ft and 47 ft

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