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The perimeter of the triangle is 84 meter. The longest side of the triangle is 7 meters less than twice the length of the shortest side, x. The middle side is 7 meters longer than the shortest side. What is the length of each side of the triangle?

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calculista

Answer:

The dimensions of triangle are

Longest side: 35 meters

Shortest side: 21 meters

Middle side: 28 meters

Step-by-step explanation:

Let

y ----> the longest side of triangle in meters

x ----> the shortest side of triangle in meters

z ----> the middle side of triangle in meters

we know that

The perimeter of triangle is equal to

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

we have

[tex]P=84\ m[/tex]

so

[tex]84=x+y+z[/tex] ----> equation A

[tex]y=2x-7[/tex] ----> equation B

[tex]z=x+7[/tex] ----> equation C

solve the system by substitution

substitute equation B and equation C in equation a

[tex]84=x+(2x-7)+x+7[/tex]

solve for x

[tex]84=4x[/tex]

[tex]x=21\ m[/tex]

Find the value of y

[tex]y=2(21)-7=35\ m[/tex]

Find the value of z

[tex]z=21+7=28/ m[/tex]

therefore

The dimensions of triangle are

Longest side: 35 meters

Shortest side: 21 meters

Middle side: 28 meters

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