Question: The height of a triangle is the successor of the number that is one-third its base. The area of the triangle is 45 sq.ft. Find its base and height.
A ) base = 16ft, height = 25ft B ) base = 13ft, height = 15ft C ) base = 5ft, height = 3ft D ) base = 15ft, height = 6ft
Steps to derive
1 Let b = base of triangle, then height h = 13b + 1
2 A = 12bh [Area = 12× base × height.]
3 45 = 12b( 13b + 1)
4b²6+b2 = 45
5b2 + 3b - 270 = 0
6 (b + 18)(b - 15) = 0
7b = - 18 or b =15
8 The base of triangle cannot be negative. So, b = 15.
