Solve the problem.
-One side of a triangle is $4 \mathrm{~cm}$ shorter than the base, $x$ . The other side is $3 \mathrm{~cm}$ longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least $29 \mathrm{~cm}$ ?

Question

Solve the problem.
-One side of a triangle is $4 \mathrm{~cm}$ shorter than the base, $x$. The other side is $3 \mathrm{~cm}$ longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least $29 \mathrm{~cm}$ ?
A) $x>6$
B) $\mathrm{x} \leq 13$
C) $0<\mathrm{x} \leq 10$
D) $\mathrm{x} \geq 10$

Quizplus · Accepted Answer

The perimeter of the triangle is at least $29 \mathrm{~cm}$, so $x+4+x+3 \geq 29$. Simplifying, $2x+7 \geq 29$, so $2x \geq 22$. Dividing by $2$, $x \geq 11$. Therefore, the base must be at least $11 \mathrm{~cm}$ long.

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