Question

If the perimeter of this triangle is to be no more than 77 feet, write an inequality and

Answer 1

Given:

Consider the sides of the triangle are 4x+10, 2x-5 and 18 (in feet).

Perimeter of this triangle is to be no more than 77 feet.

To find:

The inequality and solution of the inequality.

Solution:

Perimeter of a triangle is the sum of all side.

Perimeter of given triangle $=(4x+10)+(2x-5)+18$

Perimeter of this triangle is to be no more than 77 feet. It means perimeter must be less than or equal to 77.

$(4x+10)+(2x-5)+18\leq 77$

$(4x+2x)+(10-5+18)\leq 77$

$6x+23\leq 77$

$6x\leq 77-23$

$6x\leq 54$

Divide both sides by 6.

$x\leq \dfrac{54}{6}$

$x\leq 9$

Therefore, the required inequality is $(4x+10)+(2x-5)+18\leq 77$ and the solution is $x\leq 9$.