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Travka [436]
3 years ago
8

The perimeter of a triangle is 84. The longest side is 7 meters less than twice the length of the shortest side, x. The middle s

ide is 7 meters longer than the shortest side. What is the length of each side?
Mathematics
1 answer:
elixir [45]3 years ago
4 0
Perimeter = Side + Side + Side
Side 1 = x
Side 2 = x + 7
Side 3 = 2x-7

Plug into the equation:
84 = x + (x + 7) + (2x-7)
84 = x + x + 7 + 2x - 7

Combine like terms:
84 = 4x

Divide by 4 and solve for x:
21 = x

Side 1 = 21

Side 2 = 28
21+7=28

Side 3 = 35
21(2) - 7 = 42 - 7 = 35
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A line is drawn so that it passes through the points (-3, -1) and (4, 2).
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Answer:

(A) \boxed{\bold{y=\frac{3}{7}x+\frac{2}{7}}}

(B) \boxed{\bold{2 \ = \ \frac{3}{7} * \ 4 \ + \ \frac{2}{7}  }}

Explanation:

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Slope = \bold{\frac{y_2-y_1}{x_2-x_1}}

\bold{\left(x_1,\:y_1\right)=\left(-3,\:-1\right),\:\left(x_2,\:y_2\right)=\left(4,\:2\right)}

M = \bold{\frac{2-\left(-1\right)}{4-\left(-3\right)}: \ \frac{3}{7} }

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\bold{y=\frac{3}{7}x+b}

Plug in \bold{\left(-3,\:-1\right)\mathrm{:\:}\quad \:x=-3,\:y=-1}

\bold{-1=\frac{3}{7}\left(-3\right)+b}

Isolate B

\bold{-1=\frac{3}{7}\left(-3\right)+b}

b = \bold{\frac{2}{7} }

(B) 4 = x, 2 = y

2 = 3/7 * 4 + 2/7

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