Geometric or real-world application leading to a quadratic equation

The question describes a geometric figure, physical scenario, or word problem whose setup yields a quadratic equation to solve for a measurement such as length, area, or perimeter.

turkey-yks 2017 Q5 View
The numbers $\frac { x } { y }$, $x - y$, and $x$ are three consecutive even integers arranged from smallest to largest.\ Accordingly, what is the sum $\mathrm{x} + \mathrm{y}$?\ A) 8\ B) 10\ C) 12\ D) 14\ E) 16
turkey-yks 2020 Q21 View
In a neighborhood with 95 buildings, each building is either 2 or 3 stories. Within the scope of urban renewal, 15 of these buildings are demolished and replaced with 5-story buildings each, and the total number of stories of the buildings in the neighborhood increases from 240 to 274.
Accordingly, by what percentage did the number of 3-story buildings in the neighborhood decrease as a result of urban renewal?
A) 16
B) 18
C) 20
D) 22
E) 24
turkey-yks 2020 Q23 View
Duygu, who starts running on a running course, takes a break to rest after running a certain distance.
After the break, Duygu
  • if she runs 240 meters more, she will have run $\frac{7}{12}$ of the entire course,
  • if she runs $\frac{1}{3}$ of the distance she ran before, she will have run $\frac{3}{5}$ of the entire course.

Accordingly, what is the length of the entire course in meters?
A) 1440
B) 1620
C) 1800
D) 1980
E) 2160
turkey-yks 2020 Q27 View
A group of students, each 7 years old, visited a botanical garden in 2015; another group of students, each 10 years old, visited in 2020. The official who guided the groups through the garden said about the same historical tree in the garden to both groups: ``The age of this tree is equal to the sum of all of your ages.''
From these two groups, if the number of students in the first group is 10 more than the number of students in the second group, how old is this tree in 2020?
A) 220
B) 230
C) 240
D) 250
E) 260
turkey-yks 2023 Q20 View
Uncle Ahmet has a rectangular field with side lengths $x + 20$ and $2x + 30$ meters. He grows sunflowers in a square-shaped part with side length $x$ meters as shown in the figure.
If the area of the remaining part of the field is 1400 square meters, what is the perimeter of the entire field in meters?
A) 148 B) 154 C) 160 D) 166 E) 172