Find the area of a triangle whose sides are 28cm, 21cm and 35cm.
Also, find the length of the altitude corresponding to the largest side
of the triangle.
Answers
Answer:
- Area of triangle = 294 cm²
- Length of altitude on hypotenuse = 16.8 cm
Explanation:
Given three sides of the triangle,
- Let, AB = 28 cm, BC = 21 cm, AC = 35 cm
To find,
- Area of triangle
- Altitude corresponding to the largest side
So,
Using the converse of Pythagoras theorem
[If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.]
We have three sides,
→ AB² + BC² = AC²
→ 21² + 28² = 35²
It means the triangle formed by these lines will be a right-angled triangle.
With AC = 35 cm as hypotenuse and AB and BC other two sides.
Using the formula to calculate the area of a triangle
→ Area = 1/2 × base × height
→ Area = 1/2 × 21 × 28
→ Area = 294 cm²
Further., [Refer to the attachment]
Using the Altitude on hypotenuse theorem
[If a perpendicular is drawn from the right-angled vertex of a right triangle to the hypotenuse, then the triangles formed on both sides of the perpendicular are similar to each other and also to the whole triangle.]
In the figure AD is the perpendicular on hypotenuse BC that is the largest side so,
→ Δ ABC ~ ΔDBA
So, by corresponding parts of similar triangles
→ BC / AC = AB / AD
putting known values
→ 35 / 28 = 21 / AD
→ AD = 21 × 28 / 35
→ AD = 16.8 cm
Therefore,
- Area of the triangle will be 294 cm²., and
- Length of the corresponding altitude on the hypotenuse (largest side) will be 16.8 cm.
Step-by-step explanation:
if the area of the triangle is 294 CM square and its largest side is 35 cm find the altitude corresponding to the largest side