the perimeter of a triangular field is 280 dm. If two of its sides are 78 dm and 50 dm,find the length of the perpendicular on the side of length 50 dm from the opposite vertex.

Asked by saanvichhikara07 | 23rd Sep, 2020, 08:10: AM

Expert Answer:

The question must be:
The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.
Solution:
Let the third side be 'a'
Perimeter = 240
78+50+a = 240
a = 112
Using Heron's formula, we have
Area space of space triangle equals square root of straight s open parentheses straight s minus straight a close parentheses open parentheses straight s minus straight b close parentheses open parentheses straight s minus straight c close parentheses end root
equals square root of 120 cross times open parentheses 120 minus 112 close parentheses open parentheses 120 minus 78 close parentheses open parentheses 120 minus 50 close parentheses end root
equals square root of 120 cross times 8 cross times 42 cross times 70 end root
equals 1680 space cm squared
Area space of space straight a space triangle equals 1 half cross times Height cross times Base
1680 equals 1 half cross times Height cross times 50
Height equals fraction numerator 1680 cross times 2 over denominator 50 end fraction equals 67.2 space dm

Answered by Renu Varma | 23rd Sep, 2020, 11:49: AM