Solve each problem. The perimeter of a triangle is 323 in. The shortest side mea

Question

Solve each problem. The perimeter of a triangle is 323 in. The shortest side measures five-sixths the length of the longest side. and the medium side measures 17 in. less than the longest side. Find the lengths of the sides of the triangle. The sum of the three angles of a triangle is 180 degree . The largest angle is twice the measure of the smallest, and the third angle measures 10 degree less than the largest. Kind the measures of the three angles. The sum of three numbers is 16. The greatest number is -3 times the least, while the middle number is four less than the greatest Find the three numbers. Witny librun has a collection of pennies. dimes, and quartets. The number of dimes is one less than twice the number of pennies. If there are 27 coins in all worth a total of $4.20. how many of each denomination of coin is in the collection? Although some problem with two unknowns can be solved by using just one variable it is often easier to use two variables, and a system of equations. The following problem. which can be solved with a system appeared in a Hindu Work that dates back to about A.D 850.(See Exercise 35.)

Explanation / Answer

You have a system of 4 equations and 4 unknowns.

Set up an augmented coeficcient matrix as shown:

x y z w =

| 1 -3 7 1 11 |

| 2 4 6 -3 -3 |

| 3 2 1 2 19 |

| 4 1 -3 1 22 |

Once you have this, either subtract row 4 from row 1 to eliminate w, and begin solving in that manner, or use your calculator to find the reduced row echelon form (rref):

x y z w =

| 1 0 0 0 5 |

| 0 1 0 0 -1 |

| 0 0 1 0 0 |

| 0 0 0 1 3 |

Where you can see that x=5, y=-1, z=0, and w=3.

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