📐 geometry

1. **State the problem:** We need to find the length of the hypotenuse of a right triangle with legs 36 and 15. 2. **Recall the Pythagorean theorem:** For a right triangle with leg

1. **State the problem:** We need to find the length of the unknown leg of a right triangle where one leg is 12.75 and the hypotenuse is 37.25. 2. **Formula used:** In a right tria

1. **State the problem:** We need to find the area of a rectangle with length $2\sqrt{27}$ cm and width $4\sqrt{3}$ cm. 2. **Formula for area of a rectangle:**

1. **State the problem:** We need to find the measure of angle $m\angle XYW$ in the given triangle $XYZ$ with exterior point $W$ on segment $XY$. 2. **Given information:**

1. **Stating the problem:** We have two parallel horizontal lines intersected by two parallel diagonal lines, creating several angles. We want to find which angle facts can be used

1. The problem asks which angle fact can be used to find angle $h$ from angle $g$ when two parallel lines are cut by transversals. 2. Important angle facts when parallel lines are

1. **Stating the problem:** Find the volume of a cuboid given its total surface area is 300 cm², length $l=7$ cm, and breadth $b=16$ cm. 2. **Formula for surface area of a cuboid:*

1. **State the problem:** We need to find the measure of angle $\angle ABD$ in the quadrilateral $ABD$ where $\angle BAD = (7x + 1)^\circ$, $\angle ABD = (2x + 36)^\circ$, and side

1. **State the problem:** We need to find the height $x$ of the tree using the given distances and the height of the person. 2. **Identify the principle:** This is a problem involv

1. **Problem statement:** Describe the transformation from triangle A to triangle B using a negative scale factor. 2. **Understanding enlargement/dilation:** An enlargement with sc

1. The problem is to understand the properties of a triangle in a simple way. 2. A triangle is a polygon with three edges and three vertices.

1. **Problem statement:** The ratio of the radii of two circles is given as 8 : 9. We need to find the ratio of their circumferences and the ratio of their areas. 2. **Formulas use

1. **Problem statement:** Find the measure of angle $\angle BDC$ in triangle $BCD$ where $\angle CBD = 60^\circ$ and $\angle C = 90^\circ$. 2. **Recall the angle sum property of a

1. **Problem statement:** We have a quadrilateral ABCD with diagonal BD splitting it into two triangles ABD and BCD. 2. Given: \(\angle CBD = 60^\circ\) and right angles at vertice

1. **Problem statement:** ABCD is a rectangle with length 16 m and width 6 m. Find angles $a$ and $b$ to the nearest degree. 2. **Recall properties of rectangles:** All angles are

1. **State the problem:** We need to find how far a unicycle will travel in 4 revolutions if its wheel diameter is 25 inches and radius is 12.5 inches. 2. **Recall the formula:** T

1. **State the problem:** Find the area of a circle with radius $r=12$. 2. **Formula:** The area $A$ of a circle is given by the formula $$A = \pi r^2$$ where $r$ is the radius.

1. **Problem Statement:** We have a ratio table for circular objects with diameters and circumferences. We need to find the missing values in the table.

1. The problem asks to select the shortcut to prove that two given triangles are similar. 2. The triangles are right-angled and share a common side, with one right angle in each tr

1. The problem asks to identify the shortcut used to prove that two triangles are similar. 2. The given information shows two triangles sharing a diagonal side and each having a ri

1. **Problem statement:** We have a right triangle ABC with a right angle at B. Given: