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levacccp [35]
3 years ago
13

The length of one leg of a right triangle is 3 feet more than the other leg. If the hypotenuse is 15 feet find the length of eac

h leg
Mathematics
2 answers:
lesya692 [45]3 years ago
7 0

Answer:

One leg = x = 9.

Other leg = x+3 = 9+3 = 12.

Step-by-step explanation:

We have given hypotenuse = 15 feet and one leg is more than other the other of a right triangle.

We need to find the each leg of the right triangle.

Let the one leg = x.

Let the other leg = x+3.

We know that, Pythagoras theorem:

Hypotenuse^{2} = Perpendicular^{2} + Base^{2}

Hypotenuse = 15, one leg(base) = x and other leg(perpendicular) = x+3.

By applying pythagoras theorem:

15^{2} = x^{2} + ( x+3)^{2}

225 = x^{2} + x^{2} + 9 +6x

225 = 2x^{2} + 6x + 9

Subtracting 9 from both sides

216 = 2x^{2} + 6x

2x^{2} + 6x -216 = 0

Taking 2 common,

x^{2} + 3x - 108 = 0

x^{2} + 12x - 9x - 108 = 0

x(x+12) - 9(x+12) = 0

(x+12) (x-9)

x = -12, x = 9.

So, we will consider positive value x = 9.

Therefore, one leg = x = 9.

Other leg = x+3 = 9+3 = 12.

melamori03 [73]3 years ago
5 0

Answer:

Leg1 = 9 and leg2 = 12

Step-by-step explanation:

<u>Points to remember</u>

<u>Pythagorean theorem</u>

Hypotenuse² = Base² + Height²

<u>To find the length of each leg</u>

It is given that, hypotenuse = 15 feet

Let base = x the height = x +3

By using Pythagorean theorem we can write,

Hypotenuse² = Base² + Height²

15²  = x² + (x + 3)²

225 = x²  + x²  + 6x + 9

2x²  + 6x + 216 = 0

x²  + 3x + 108 = 0

By solving we get x = 9 and x -12

Therefore one leg = 9 and other leg = 9 + 3 = 12

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