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1-65.

The perimeter (the sum of the side lengths) of the triangle at right is $52$ units. Write and solve an equation based on the information in the diagram.

Use your solution for $x$ to find the measures of each side of the triangle. Be sure to confirm that your answer is correct. Homework Help ✎

Find the sum of the side lengths.

$(7x − 4) + (19) + (10x + 3)$

The sum of the side lengths is the perimeter, which we know from the problem is $52$ units. Set expression from Step 1 equal to $52$ and solve for $x$.

$\left. \begin{array} { r } { ( 7 x - 4 ) + ( 19 ) + ( 10 x + 3 ) = 52 } \\ { 7 x + - 4 + 19 + 10 x + 3 = 52 } \\ { 17 x + 18 = 52 } \\ { \frac { - 18 - 18 } { 17 x } = 34 } \\ { \frac { 17 x } { 17 } = \frac { 34 } { 2 } } \\ { x = 2 } \end{array} \right.$

$(7x − 4) + (19) + (10x + 3) = 52$, If $x = 2$,
$(7 · 2 − 4) + (19) + (10 · 2 + 3) = ? = 52$
$10 + 19 + 23 = ? = 52$
$52 = 52$

$7·2−4=1019=19\ 10·2+3=23$

$10 + 19 + 23 = 52$