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2 years ago

17) The measures of two sides of a triangle are (2x + 3y) and (5x – 2y). If the perimeter

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

4 0

Answer:

5x +4y

Step-by-step explanation:

The perimeter of a triangle is the sum of side lengths. That fact can be used to find z, the length of the third side.

(2x +3y) +(5x -2y) +z = 12x +5y . . . . sum of sides is perimeter

z = (12x +5y) -(7x +y) . . . . . . . . . . . . subtract (7x+y) from both sides

z = 5x +4y . . . . . . . . . collect terms; the length of the third side

The third side of the triangle is (5x +4y).

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Step-by-step explanation:

$\left \{ {{3x^2+4y=17} \atop {2x^2+5y=2}} \right. \\\\Then\\\\\left \{ {{2 \times (3x^2+4y)=2 \times 17} \atop {3\times(2x^2+5y)=3\times2}} \right. \\\\\left \{ {{6x^2+8y=34 \quad (1)} \atop {6x^2+15y=6\quad (2)}} \right.\\\\(1)-(2) \Rightarrow -7y=28 \Rightarrow y =-4.\\Since \: \: 2x^2+5y=2 \Rightarrow 2x^2=2-5y\\\Rightarrow 2x^2=2+20=22\\\Rightarrow x^2=22:2=11\\\Rightarrow x=\pm \sqrt{11}.$

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