An isosceles triangle has an area of 125 feet. if the base is 14 feet, what is the length of each leg

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28-05-2018
Mathematics

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An isosceles triangle has an area of 125 feet. if the base is 14 feet, what is the length of each leg

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tramserran tramserran · Answer 1 · 2018-05-28T12:23:57+02:00

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 gmany · Answer 2 · 2018-05-28T12:34:50+02:00

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]