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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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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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Dec 8, 2019
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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
Mathematics
high-school
Alex Morega
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Alex Morega
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Look at the picture.
The formula of the area of a triangle is:
substitute:
Use the Pythagorean theorem
Bruno Lowagie
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Dec 9, 2019
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Bruno Lowagie
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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
Cryckx
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Dec 14, 2019
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Cryckx
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