SOLUTION: Land in the shape of an isosceles triangle has a base of 130 m. An altitude from the vertex of one of the base angles of the triangle is 120 m. What is the area of this property

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Question 1150800: Land in the shape of an isosceles triangle has a base of 130 m. An altitude from
the vertex of one of the base angles of the triangle is 120 m. What is the area
of this property
in m²?
Found 3 solutions by MathLover1, Edwin McCravy, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!


We can equate the area as follows

... (1)
.......... (2)

Set (1) = (2) and solve for the side







The side is the of a right triangle with the height and base being the legs

So, using the Pythagorean Theorem, we have that

}

Substitute




















So,










Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
 

The green line BD is the altitude drawn from vertex of base angle B, so BD is
perpendicular to AC. So ADB is a right triangle, so by the Pythagorean theorem,









CDB is also a right triangle, so also by the Pythagorean theorem,




But since BC = AD + CD
          BC = 50 + CD


















Edwin
Answer by ikleyn(52818)   (Show Source): You can put this solution on YOUR website!
.

 


Red line  CE  is the altitude in triangle ABC drawn to the base.

Green line BD is the altitude drawn from the base vertex B to the lateral side AC.


Triangle ABD is a right angled triangle with the hypotenuse of 130 meters and the leg BD of 120 meters.

Hence, it is (5,12,13)-triangle and its leg AD is 50 meters.


Thus the area of the triangle ABD is   = 3000 square meters.


Triangle ACE is similar to the triangle ABD (since they both are right angled triangles and have common acute angle A).


The similarity coefficient is the ratio of their shorter legs   = .


Therefore, the area of the triangle ACE is   = 30*169 square meters,

and the area of the triangle ABC is twice this value, i.e.  2*30*169 = 10140 square meters.    ANSWER

Solved.


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