Answer:
y = 6
Explanation:
You want the value of y, given the sides of isosceles triangle DEF are marked as (7y +14) and (9y +2).
Isosceles triangle
The sides of an isosceles triangle are congruent, so we have ...
FD = FE
7y +14 = 9y +2
12 = 2y . . . . . . . . . . subtract 7y+2
6 = y . . . . . . . . . divide by 2
The value of y is 6.
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Additional comment
We know this triangle is isosceles for a couple of reasons. One is that the altitude is a perpendicular bisector of the base. Another is that the two smaller triangles are congruent by the SAS (or LL) postulate, making FD = FE by CPCTC.
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