📐 geometry

1. **State the problem:** We have a rectangular prism ABCDEFGH with edges summing to 28 cm and total surface area 13 cm². We need to find the length of the diagonal EC. 2. **Define

1. **State the problem:** We have a rectangular prism ABCDEFGH with the sum of all edge lengths equal to 28 cm and total surface area equal to 13 cm². We need to find the length of

1. **State the problem:** We have a rectangular prism with edges summing to 28 cm and total surface area 13 cm². We want to find the length of the diagonal $EC$. 2. **Define variab

1. **State the problem:** Two students build boxes: one a cube with edge 60 cm, the other a rectangular prism with width $w$ cm, height 30 cm, and depth 45 cm. Both boxes have the

1. The problem asks to identify the quadrant of the point (8,7). 2. Recall the quadrant rules for points $(x,y)$ in the Cartesian plane:

1. **Énoncé du problème :** Montrer que la droite (DC) est l'image de la droite (AB) par la translation de vecteur \(\overrightarrow{BC}\).

1. Problem: To find the length of side BC in two similar triangles ABC and ADE, given |AE|=2, |EC|=3, and |ED|=4. 2. Since triangles ABC and ADE are similar, corresponding sides ar

1. **Stating the problem:** We have two right triangles with given side lengths and an unknown segment $x$. We need to find $x$ in each case.

1. **State the problem:** We are given the circumference $C$ of a circle as 119.32 inches and need to find the diameter $d$ of the circle, rounded to the nearest hundredth. 2. **Fo

1. **Stating the problem:** We have four points on a horizontal line: $A(1,2)$, $M(a,b)$, $N(c,d)$, and $B(10,17)$ arranged from left to right. We want to understand the relationsh

1. **Stating the problem:** We have two right triangles with sides labeled and relationships given. We want to find the values of $x$ and $y$ using the given ratios and the fact th

1. **State the problem:** We need to find the volume of a sphere with a diameter of 16 inches. 2. **Formula for the volume of a sphere:**

1. **Problem statement:** We are given two similar equilateral triangles with areas 396 cm² and 275 cm² respectively.

1. **State the problem:** We need to find the volume of a sphere with radius $r = 15$ meters. 2. **Formula for the volume of a sphere:**

1. **State the problem:** We need to find the volume of a sphere with a diameter of 8 ft. 2. **Formula for the volume of a sphere:**

1. **Stating the problem:** We have two pairs of parallel lines crossed by transversals, creating pairs of corresponding or alternate interior angles that are equal. 2. **First pai

1. **State the problem:** We need to find the volume of a sphere with a diameter of 10 meters. 2. **Formula for the volume of a sphere:** The volume $V$ of a sphere is given by the

1. **State the problem:** We need to find the volume of a sphere with a diameter of 10 meters. 2. **Recall the formula for the volume of a sphere:**

1. **State the problem:** We need to find the volume of a sphere with radius $r = 13$ ft. 2. **Formula for the volume of a sphere:**

1. **State the problem:** We need to find the volume of a sphere with radius $r = 5$ inches. 2. **Formula for the volume of a sphere:** The volume $V$ of a sphere is given by the f

1. The problem asks which figure is similar to Figure A. 2. Similar figures have the same shape but may differ in size. This means their corresponding angles are equal and their co