# The legs of a right-angled triangle are 1: 3. Find the height of a triangle dropped from the vertex

July 29, 2021 | education

| **The legs of a right-angled triangle are 1: 3. Find the height of a triangle dropped from the vertex of a right angle if the hypotenuse is 40**

1. Vertices of the triangle – A, B, C. Angle A – straight line. AE – height. S – area. AB: AC = 1: 3.

BC = 40 units.

2. AC = 3AB.

3. AB² + AC² = BC² (along the tower of Pythagoras). We substitute 3AB here instead of AC:

AB² + (3AB) ² = 1600.

AB² + 9AB² = 1600.

AB² = 160.

AB = 4√10 units of measurement.

AC = 3 x 4√10 = 12√10 units of measurement.

4. S = AB x AC / 2 = 4√10 x 12√10 / 2 = 240 units.

5.S = BC x AE / 2.

AE = 2 x 240: 40 = 12 units.

Answer: AE height is 12 units.

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