📐 geometry

1. The problem asks for the scale factor (as a ratio) of Figure B to Figure A based on the side lengths of two triangles. 2. The scale factor between two similar figures is the rat

1. The problem states that triangles $\triangle GHJ$ and $\triangle LMK$ are similar with a scale factor of $\frac{5}{6}$ from $\triangle LMK$ to $\triangle GHJ$. We are asked to f

1. **Problem Statement:** We have triangle $\triangle PQR$ with circumcenter $V$ where the perpendicular bisectors $SV$, $TV$, and $UV$ intersect. Given: $UV=30$, $PS=64$, and $RV=

1. **Problem Statement:** We have triangle $\triangle XYZ$ with circumcenter $S$, where $S$ is the intersection of the perpendicular bisectors $\overline{TS}$, $\overline{US}$, and

1. **Problem Statement:** We have triangle $\triangle TUV$ with circumcenter $D$, where $D$ is the intersection of the perpendicular bisectors $AD$, $BD$, and $CD$. Given lengths:

1. **Problem statement:** Given two parallel lines $m \parallel n$ cut by a transversal, find the values of $x$ and $y$ given the angles: - On line $m$: angle $= (8x + 13)^\circ$

1. **Problem Statement:** Find the measures of angles $m\angle 1$ through $m\angle 48$ given the polygon with vertices and internal polygons: a regular hexagon BCEFJ, a regular pen

1. **State the problem:** We want to find the total length $L$ of the string in a ball of string with radius $r = 2$ m. 2. **Formula and assumptions:** The ball is roughly a sphere

1. **Problem statement:** Calculate the circumference, surface area, and volume of Earth modeled as a sphere with radius $r = 6.37 \times 10^6$ meters. 2. **Formulas:**

1. **Problem statement:** We have a right triangle formed by a lamp of height 3 m, a building of height $H$ meters, and the horizontal distance between them is 20 m. We need to fin

1. **Problem Statement:** We have a triangle with vertices K(-1,-2), L(-1,2), and M(2,-2). We need to find the coordinates of the vertices after a dilation centered at the origin w

1. **State the problem:** We want to find how many boxes of size 29 inches by 20 inches by 15 inches can fit on a pallet of size 40 inches by 48 inches, stacked up to 15 feet high.

1. The problem is to find the volume of a box with dimensions 29 inches by 20 inches by 15 inches. 2. The formula for the volume $V$ of a rectangular box is:

1. **State the problem:** We need to find the volume of a cylindrical pole with height $20$ m and base radius $7$ m. 2. **Formula used:** The volume $V$ of a cylinder is given by t

1. **State the problem:** We need to find the total surface area of a closed box with a base of 15m by 15m and a height of 7.5m. 2. **Formula for total surface area of a closed rec

1. Statement of the problem: The relation between the sum $y$ of the interior angles of a polygon and the number of its sides $x$ is given by the formula below. $$y = \pi(x - 2)$$.

1. **State the problem:** We are given a triangle with angles $115^\circ$, $(4k + 5)^\circ$, and $(6k + 10)^\circ$. We need to find the value of $k$. 2. **Recall the Triangle Angle

1. **Problem statement:** In the figure, ABCD is a parallelogram with the same base BC and between the same parallel lines AD and BC. (a) Write the relation between the area of tri

1. **Énoncé du problème :** On considère un triangle $ABC$ avec $I$ milieu de $[AB]$ et $J$ milieu de $[AC]$.

1. **Énoncé du problème :** Construire les points D et K définis comme barycentres des points pondérés (A ; 5) et (B ; 2).

1. **Problem Statement:** Given a rectangle PQRS and a parallelogram TQRU inside it, with RV perpendicular to TQ, we need to find the relation between the areas of PQRS and TQRU, p