One leg of a right triangle is 3 meters shorter than the other leg. If the hypotenuse is 14 meters, find the length of the two legs. Approximate your answers to the nearest tent…

Question

asked Nov 23, 2020 102k views

1 Answer

Ayhan · Answer 1 · 2020-11-29T08:09:00+0000

Answer: Length of one leg =x = 11.3 m

Length of another leg = 11.3-3 = 8.3 m

Explanation:

Let one leg of the right triangle be x , then the other leg be x-3.

Hypotenuse = 14 meters

Pythagoras theorem of right -triangle says that he square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

Then for the given situation , we have

$(14)^2=x^2+(x-3)^2\\\\\Rightarrow\ 196=x^2+x^2+3^2-2(3)x\\\\\Rightarrow\ 196=2x^2+9-6x\\\\\Rightarrow 2x^2+9-6x-196=0\\\\\Rightarrow 2x^2-6x-187$

Which is a quadratic equation.

For quadratic equation
ax^2+bx+c , the root of equation is
$x=(-b\pm√(b^2-4ac))/(2a)$

In
2x^2-6x-187 , a= 2 , b= -6 and c=-187 , then

$x=(-(-6)\pm√((-6)^2-4(2)(-187)))/(2(2))$

$x=(6\pm√(1532))/(4)$

$x\approx(6\pm 39.14)/(4)\\\\ x=(6+39.14)/(4)\ or\ x=(6-39.14)/(4)$

$\\\\ x=11.285\ or\ x=-8.285$

Side cannot be negative , so avoid x=-8.285.

so
$x=11.285\approx11.3$

⇒ Length of one leg =x = 11.3 m

Length of another leg = 11.3-3 = 8.3 m