Question

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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.

Answer 1

#10

• Perimeter=sum of sides

`\\ \rm\Rrightarrow 7+0.5x+x-8=50`

`\\ \rm\Rrightarrow 1.5x-1=50`

`\\ \rm\Rrightarrow 1.5x=51`

`\\ \rm\Rrightarrow x=34`

• Smallest side should be 7units

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

#11

`\\ \rm\Rrightarrow x+1+21+0.5x=75`

`\\ \rm\Rrightarrow 1.5x+22=75`

`\\ \rm\Rrightarrow 1.5x=53`

`\\ \rm\Rrightarrow x=35.3`

• 0.5x=17.6
• x+1=36.3

Smallest side 21units

Answer 2

Question 10

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

Input found value of x to determine side lengths:

`\implies 7`

`\implies (1)/(2)(34)=17`

`\implies 34-8=26`

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

Question 11

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

Input found value of x to determine side lengths:

`\implies 21`

`\implies (1)/(2)\left((106)/(3)\right)=(53)/(3)=17(2)/(3)`

`\implies (106)/(3)+1=(109)/(3)=36(1)/(3)`

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