Question

Triangle DOG i an iocele with bae angle D and G. Line egment DO i one more than the quare of a number, and line egment OG i two le than four time a number. Line egment DG i three le than twice the number. Find the number, the length of the leg, and the length of the bae

Answer 1

• the number is 3
• DO = OG = 10
• DG = 3

Explanation:

Given isosceles triangle DOG with DO≅GO, DO = (n²+1), GO = (4n-2) and DG = (2n -3), you want the value of n and the lengths of the sides.

Setup

The expressions for the congruent sides will have the same value, so ...

DG -GO = 0

(n² +1) -(4n -2) = 0

Solution

n² -4n +3 = 0 . . . . . . . . simplify

(n -3)(n -1) = 0 . . . . . . factor

n = 1 or 3 . . . . . . . . values of n that make the factors zero

The length of leg DG is ...

2n -3 = 2{1, 3} -3 = {2, 6} -3 = {-1, 3}

Side DG cannot be negative, so the "solution" n = 1 is extraneous.

GO = 4n -2 = 4(3) -2 = 10

The number is 3, the leg lengths are DO = OG = 10, and the base length is DG = 3.