one leg of a right triangle is 42 inches longer than the other leg, and the hypotenuse is 78 inches what is the length of the legs of the triangle

Answer 1

Hi Laynie C.,

Let x = the length of the other leg

Let x + 42 = the length of the longer leg

And for right triangles we can use the Pythagorean Theorem a² + b² = c² to find x. With a or b either one if the legs and c is the hypotenuse:

x² + (x + 42)² = 78², can you solve it from here?

You will end up with +30 inches and -72 inches, use the positive value.

Remember, your solution will be x, which equals the length of the other leg. You will still need to find the length of the longer leg, x + 42, for the solution to the lengths of both legs.

Let me know, Joe.

Answer 2

Using the Pythagorean Theorem (because its a right triangle) we can calculate the legs using the following formula:

a^2 + b^2 = c^2 where c is the hypotenuse and a & b are the other legs of the triangle

1. a^2 + (a+42)^2 = 78^2

we foil the (a+42)^2 :

1. a^2 + a^2 + 84a + 1764 = 6084

combining like terms:

1. 2a^2 + 84a + 1764 = 6084

Moving terms around

1. 2a^2 + 84a - 4320 = 0

Factoring the left side of the equation:

1. 2(a-30)(a+72)

Setting each factor equal to zero we can see that a will be either:

1. a=30 or a= -72

Since we cant have a negative length for our triangle, a = 30

meaning to find the other leg we take

1. a+42 = 72

So the lengths are

1. a = 30
2. b = 72
3. c = 78

Let's check our work by plugging these values back into our Pythagorean Theorem

1. a^2 + b^2 = c^2
2. (30)^2 + (72)^2 = (78)^2
3. 900 + 5184 = 6084

The math checks out. I hope this helps.