Question

the perimeter of the triangle below is 52 units. fill in the missing blanks for the equation below that you could use to solve for x. 10x + 3+19 + ____x - 4 = __. what is the length of the shortest side? __ units. what is the length of the longest side? __ units. what is the value of x? ____. blank 1: blank 2: blank 3: blank 4: blank 5:

Explanation:

Step1: Recall perimeter formula

The perimeter of a triangle is the sum of the lengths of its sides. So, the equation for the perimeter of this triangle is $(10x + 3)+19+(7x - 4)=52$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side: $(10x+7x)+(3 + 19-4)=52$, which simplifies to $17x+18 = 52$.

Step3: Solve for $x$

Subtract 18 from both sides of the equation: $17x=52 - 18$, so $17x=34$. Then divide both sides by 17: $x = 2$.

Step4: Find side lengths

For the side $7x - 4$, substitute $x = 2$: $7\times2-4=14 - 4=10$.
For the side $10x + 3$, substitute $x = 2$: $10\times2+3=20 + 3=23$.
The side lengths are 10, 19, and 23. The shortest side is 10 units and the longest side is 23 units.

Answer:

Blank 1: 7
Blank 2: 52
Blank 3: 10
Blank 4: 23
Blank 5: 2