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10. The perimeter of a triangle is 50 and the side lengths are 7, 1/2x and x - 8. Solve for x. What is the length of the smallest side?


11. The perimeter of a triangle is 75 and the side lengths are 21, 1/2x, x + 1. Solve for x. Find the length of the smallest side.

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semsee45

Answer:

Question 10

[tex]\begin{aligned}\textsf{Perimeter} & = 50\\\\\implies 7 + \dfrac{1}{2}x+(x-8) & = 50\\\\\dfrac{3}{2}x & =51\\\\x & = 34\end{aligned}[/tex]

Input found value of x to determine side lengths:

[tex]\implies 7[/tex]

[tex]\implies \dfrac{1}{2}(34)=17[/tex]

[tex]\implies 34-8=26[/tex]

Therefore, the length of the smallest side is 7 units.

Question 11

[tex]\begin{aligned}\textsf{Perimeter} & = 75\\\\\implies 21 + \dfrac{1}{2}x+(x+1) & = 75\\\\\dfrac{3}{2}x & =53\\\\x & = \dfrac{106}{3}\end{aligned}[/tex]

Input found value of x to determine side lengths:

[tex]\implies 21[/tex]

[tex]\implies \dfrac{1}{2}\left(\dfrac{106}{3}\right)=\dfrac{53}{3}=17\frac{2}{3}[/tex]

[tex]\implies \dfrac{106}{3}+1=\dfrac{109}{3}=36\frac{1}{3}[/tex]

Therefore, the length of the smallest side is 17 ²/₃ units.

#10

  • Perimeter=sum of sides

[tex]\\ \rm\Rrightarrow 7+0.5x+x-8=50[/tex]

[tex]\\ \rm\Rrightarrow 1.5x-1=50[/tex]

[tex]\\ \rm\Rrightarrow 1.5x=51[/tex]

[tex]\\ \rm\Rrightarrow x=34[/tex]

  • Smallest side should be 7units

As 0.5x=17units and x-8=26units

#11

[tex]\\ \rm\Rrightarrow x+1+21+0.5x=75[/tex]

[tex]\\ \rm\Rrightarrow 1.5x+22=75[/tex]

[tex]\\ \rm\Rrightarrow 1.5x=53[/tex]

[tex]\\ \rm\Rrightarrow x=35.3[/tex]

  • 0.5x=17.6
  • x+1=36.3

Smallest side 21units

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