SOLUTION: In a right triangle, the perimeter is 70, and the sum of the squares of the sides is 1682. Find the lengths of the three sides. Thanks for your help.

Question 924439: In a right triangle, the perimeter is 70, and the sum of the squares of the sides is 1682. Find the lengths of the three sides. Thanks for your help.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
There are two solutions to this problem, we are given
a + b +c = 70 and a^2 +b^2 +c^2 = 1682
note that a^2 +b^2 = c^2(right triangle), therefore we have
c^2 +c^2 = 1682
2c^2 + 1682
c^2 = 841
c = 29
note we are dealing only with positive roots
now we have
a +b +29 =70
a +b = 41
a^2 +b^2 +841 = 1682
a^2 +b^2 = 841
now solve a +b = 70 for b and substitute b in a^2 +b^2 = 841
a^2 +(41-a)^2 = 841
a^2 +1681 -82a +a^2 = 841
2a^2 -82a +840 = 0
a^2 -41a +420 = 0
factor this equation
(a-21)*(a-20) = 0
a =21 or 20
our two solutions are
a=21, b=20, c=29
a=20, b=21, c=29

RELATED QUESTIONS
the perpendicular sides of a right-angled triangle have lengths in the ratio 3:4. The... (answered by josgarithmetic)

The perimeter of a right triangle is 42 and the sum of the squares of its 3 sides is 722. (answered by Alan3354,ikleyn)

The perimeter of a right triangle is 42 and the sum of the squares of its sides is 722.... (answered by Alan3354,ikleyn)

The perpendicular sides of a right-angles triangle have lengths in the ratio 3:4. The... (answered by Alan3354)

The sum of the squares of the lengths of the three sides of a right triangle is 300 cm2.... (answered by Earlsdon)

The lengths of the sides of a triangle are three consecutive integers. If the perimeter... (answered by EMStelley,josmiceli)

is the triangle of three sides of unit lengths 6, 11 and 9 a right... (answered by Alan3354)

The perimeter of a triangle is 42 inches. The lengths of the sides are represented by... (answered by Earlsdon)

An isosceles triangle is a triangle with two sides having the same measurement and one... (answered by macston)