Question

A triangle has side lengths of 11 cm and 9 cm. Which could be the value of the third side, 20 cm or 15 cm?

There are several vendors at the carnival who sell products and also advertise their businesses.
​Steve works for a recreational company that sells ATVs, dirt bikes, snowmobiles, and motorcycles.
​
​His boss paid him $500 for working all of the days at the carnival plus 5% commission on all of the sales made at the carnival.
​
​What was the minimum amount of sales Steve needed to sell if he earned more than $1,500?

Answer 1

Length of Third Side = 15 cm,

Steve Sold More than $ 20,000

Explanation:

1 . Consider the Triangle Inequality Theorem, as to solve for the length of the third side;

`Triangle Inequality Theorem -\\\\| a - b | < c < a + b,\\| c - a | < b < c + a,\\| c - b | < a < c + b,\\\\Say, a = 11 cm, b = 9 cm, c = 20 -\\\\11 - 9 < 20 < 11 + 9,\\20 - 11 < 9 < 20 + 11,\\20 - 9 < 11 < 20 + 9\\\\As 20 = 20, not 20 < 20 -\\Conclusion ; Length of Third Side = 15 cm`

2 . Consider c - commission $;

`5percent - FractionForm, -\\5 / 100 - Simplified -\\1 / 20,\\`

`Inequality - 500 + 1 / 20 * c > 1,500,\\500 + 1 / 20 * c > 1,500 =\\1 / 20c > 1,000,\\c > 20,000 -\\Conclusion ; Steve Sold More Than 20,000 Dollars`

Answer 2

Explanation:

third side is <11+9 or <20cm

or >11-9 or >2

so third side=15 cm

Let x be the sale.

Then 500+.05x>1500

.05x>1500-500

.05 x>1000

x>$2000

minimum sale=$2000