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Whitepunk [10]
3 years ago
5

The perimeter of a triangular garden is 66 feet. Find the length of the three sides if the middle length side is 4 feet greater

than twice the length of the smallest side, and the longest side is 4 feet less than 3 times the length of the smallest side.
Mathematics
1 answer:
Georgia [21]3 years ago
4 0

Answer:

11 feet, 26 feet, 29 feet

Step-by-step explanation:

(2x+4 middle) + (3x- 4 longest)  + (x smallest )= 66

2x +3x +x +4 - 4= 6x

6x = 66

x= 66/6

x = 11

smallest = 11 feet

middle = 2(11) + 4 =   26 feet

longest = 3(11) -4 = 29 feet

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Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

$y-y_{1}=m\left(x-x_{1}\right)$

Substitute $-\frac{1}{3}$ for m,-1 for $x_{1}$, and 4 for $y_{1}$ in the above equation and simplify using the distributive property as follows,

y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$

Step 3 of 3

Simplify the equation further.

Add 4 on each side of the equation $y-4=\frac{1}{3} x-\frac{1}{3}$, and simplify as follows,

y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$

This is the required linear equation.

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