To find the area of triangle ADE, we need to first find the lengths of its sides.
Since triangle ABC is a right triangle, we can use the Pythagorean theorem to find the length of BC.
According to the theorem:
BC^2 = AB^2 + AC^2
BC^2 = 6^2 + 8^2
BC^2 = 36 + 64
BC^2 = 100
BC = √100
BC = 10 cm
Since BCDE is a square and BC is one of its sides, all the other sides of the square are also equal to BC. Therefore, DE = 10 cm.
To find the area of triangle ADE, we need the height of the triangle. The height is the length of the perpendicular line segment from vertex A to side DE.
Since triangle ABC is a right triangle, the altitude from right angle B divides the triangle into two smaller triangles, ABD and ACD, which are similar to the original triangle ABC.
The ratio of the sides of these similar triangles is:
AB/BD = AC/CD
6/BD = 8/(BC - BD)
6/BD = 8/(10 - BD)
6(10 - BD) = 8BD
60 - 6BD = 8BD
60 = 14BD
BD = 60/14
BD ≈ 4.286 cm
The height of triangle ADE is BD, which is approximately 4.286 cm.
Now we can calculate the area of triangle ADE using the formula:
Area = (1/2) * base * height
Area = (1/2) * DE * BD
Area = (1/2) * 10 * 4.286
Area ≈ 21.43 cm²
Therefore, the area of triangle ADE is approximately 21.43 square centimeters.
Right triangle ABC has legs AB = 6 cm and AC = 8 cm. Square BCDE is drawn
outside of the triangle along the hypotenuse. What is the area of triangle ADE?
1 answer
1 answer