SOLUTION: the perimeter of a right triangle is 90 ft. the ratio of the legs is 5:12. what is the length of the longest leg of the triangle?

Question 621037: the perimeter of a right triangle is 90 ft. the ratio of the legs is 5:12. what is the length of the longest leg of the triangle?
Answer by matt501823(7) (Show Source): You can put this solution on YOUR website!
The pythagorean Theorem is . If you substitute in 5 and 12 for a and b respectively you get . . Thus the ratios of the sides must be 5, 12, and 13. Now we know that in order to maintain this ratio we must multiply the sides by a common factor such that the perimeter equals 90. To do this we can create the following equation:
. We can further simplify this equation so it becomes . Now we must divide both sides of the equation by 30, so we get . Now that we know that the common factor is 3 we can simply multiply the side length with a ratio of 13 by 3 and we get . Thus, the side lengths must be 15, 36, and 39 as . The longest side of the three is 39, so 39 is the answer.
RELATED QUESTIONS
the perimeter of a right triangle is 90 feet. the ratio of the legs is 6:8. what is the... (answered by checkley77)

the perimeter of a right triangle is 90 feet. the ratio of the legs is 5:12. what is the... (answered by ankor@dixie-net.com)

The perimeter of a right triangle is 12 ft, and one of its legs measures 3 ft. Find the... (answered by mananth)

The legs of a right triangle are in a ratio of 7 to 11. If the perimeter is 2015 cm, what (answered by Boreal,josmiceli)

In a right triangle, the ratio of the legs is one to two. If the area of the triangle is... (answered by josmiceli)

The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of... (answered by ewatrrr)

2 legs of a right triangle are in the ratio of 5:6. The hypotenuse is 61. If the longer... (answered by stanbon)

The hypotenuse of a right triangle is 7 ft long. One leg is 1.4ft longer than the other... (answered by josgarithmetic,ikleyn)