# Triangle Perimeter

Pro Problems > Math > Algebra > Equations > Systems of Equations > Word Problems## Triangle Perimeter

The shortest side of a triangle has length 16 inches. The perimeter of the triangle is nineteen less than three times the longest side.The remaining side is eight inches shorter than the longest side. What are the side lengths of the triangle?

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.## Similar Problems

### Sum of Two Fractions

### Antique Table Price

The price of an antique table varies directly with age of the antique (in years) and with the surface area (in square feet). The price varies inversely with the number of scratches on the surface. A table which is 120 years old, is 3 feet x 8 feet , and has n scratches on the surface, costs $4,320. A table which is 140 years old, is 4 feet x 8 feet, and has n - 1 scratches on the surface, costs $7,680. If a table 150 years old, which is 4 feet x 6 feet , costs $10,800, how many scratches are on the surface?

### Handshakes

Mr. T wants each of his math students to shake hands with each of his other math students exactly once. He also wants each of his math students to shake Mr. H's hand twice. Mr. T shakes Mr. H's hand once. If there were 78 handshakes in all, how many math students does Mr. T have?

### Spiders and ants

In my house there are both ants and spiders. Together there are 240 legs. If there were half as many spiders, and twice as many ants, there would be 336 legs. How many ants do I have in my house?

### Chickens and Roosters

My neighbor has both chickens and roosters. He has a total of 31 birds. The number of chickens is ten more than twice the number of roosters. How many chickens does he have?

### Humpty Dumpty

The reason the king's horses and the king's men couldn't put Humpty Dumpty back together again is that the king's horses were no help whatsoever. In fact, the king's horses (who are not very handy) accidentally break pieces instead of putting them together.

One king's man can put together two pieces every 5 seconds.

One king's horse can break a piece in two every 2 seconds.

There are twenty more men than horses.

If there had been six fewer men, and horses broke pieces at a rate of one every three seconds, they could have done the job.

If the number of men and the number of horses are both prime numbers, how many men and horses are there?

### Henry's Books

Henry has five books. The third book has 100 fewer pages than the first and second books combined. The fourth book has 50 pages more than twice the number of pages in the first book. The last book has 150 fewer pages than three times the second book. In all, his books have 748 pages. Together, his first and second books have 216 pages. How many pages does his largest book have?

### Three Digits by Sums

I am a three digit number. The sum of my first two digits is 15, and the sum of my last two digits is 8. The sum of my first and last digits is 7. What number am I?

### Six more than Twice the Smaller

The sum of two numbers is six more than twice the smaller number, and if the larger number is multiplied by three, the result is ten less than seven times the smaller number. What is the larger number?

### Difference and Sum

Two numbers add to twenty-seven more than the opposite of the smaller number. The numbers differ by three. What is the larger number?