Advanced Mathematics Problems: Quadratic Equations

Which values correctly represent the base and the height of a right triangle contraining 510 ft^2 in which the base is 4 ft shorter than the height?

A. Base = 16 ft Height = 20 ft
B. Base = 25 ft Height = 29 ft
C. Base = 30 ft Height = 34 ft
D. Base = 32 ft Height = 36 ft

Solution:

The formula for the area of a right triangle is

A= bh/2

B is the base of the triangle and h is its height. In this problem, the base is 4 ft less than the height.

B= h-4

A= (h-4)h/2 = 510 ft^2

H^2-4h/2 = 510

H^2-4h = (510)(2)

H^2 - 4h = 1020

H^2 - 4h - 1020 = 0

Use the quadratic formula to find the two roots of the expression.

H = -b ± √b^2 - 4ac/ 2a

= -(-4) ±√(-4)^2 - (4)(1)(-1020)/ (2)(1)

= 4 ± √16+4080/2

= 4 + 64/2 and 4-64/2

= 34 ft (height)

= 30 ft (base)

Answer is C.

This is problem 4 (2-1) from the NEW third edition of “Surveying Solved Problems for the FS and PS Exams” by Jan Van Sickle, PLS (formerly "1001 Solved Surveying Fundamentals Problems"). Reprinted with permission from “Surveying Solved Problems for the FS and PS Exams” by Jan Van Sickle, PLS (2008 Professional Publications Inc.). For details on this and other FLS exam-prep books, call 800/426-1178 or visit www.ppi2pass.com