Respuesta :

tramserran
Area of a right triangle is (1/2) x base x height
Cut the isosceles triangle in half to create a 90° triangle.
Then, (1/2)Area = (1/2) base x height
           (1/2)(125) = (1/2) (14/2) x height
                    125  =             7     x    h
                  125/7  =  h

Now use Pythagorean Theorem to find the hypotenuse (c):
a² + b² = c²
(7)² + (125/7)² = c²
49 +  318.88  = c²
    367.88       = c²
     19.18        = c
Since it is an isosceles triangle, the legs are the same length.

Answer: the length of each leg is ≈ 19.18



gmany
Look at the picture.
The formula of the area of a triangle is: [tex]A_\Delta=\dfrac{1}{2}bh[/tex]
[tex]b=14\ ft.;\ A_\Delta=125\ ft.[/tex]
substitute:
[tex]\dfrac{1}{2}\cdot14\cdot h=125\\\\7h=125\ \ \ |:7\\\\h=\dfrac{125}{7}\ ft.[/tex]

Use the Pythagorean theorem
[tex]l^2=\left(\dfrac{14}{2}\right)^2+\left(\dfrac{125}{7}\right)^2\\\\l^2=7^2+\dfrac{15625}{49}\\\\l^2=49+\dfrac{15625}{49}\\\\l^2=\dfrac{2401}{49}+\dfrac{15625}{49}\\\\l^2=\dfrac{18026}{49}\\\\l=\sqrt{\dfrac{18026}{49}}\\\\l=\dfrac{\sqrt{18026}}{7}\approx19.18\ ft.[/tex]
Ver imagen gmany

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