📐 geometry

1. **State the problem:** Lin's walking path forms a triangle with vertices at the gym (G), his house (H), and the lecture hall (L). We know the sides: $GH=615$ ft, $GL=910$ ft, an

1. **State the problem:** Ramon has two wood pieces 7 inches and 3 inches long, and he wants to cut a third piece that is the longest side to form an acute triangle. We need to fin

1. **State the problem:** Marlena has three straws with lengths 12 inches, 9 inches, and an unknown shortest straw length $x$. The three straws form an obtuse triangle. We need to

1. **State the problem:** Janice estimates the longest side of a triangle with sides 16 and 20 to be 25 units if it's a right triangle. We need to compare this estimate with the ac

1. The problem is to classify the triangle with sides 7 ft, 15 ft, and 17 ft as right, acute, or obtuse. 2. Recall the classifications based on side lengths using the Pythagorean t

1. **State the problem:** Determine the type of triangle with side lengths 10, 11, and 15. 2. **Identify the sides:** The sides are $10$, $11$, and $15$. We apply the triangle clas

1. State the problem: We have two triangles, JKL with sides 3, 6, 4 and XYZ with sides 4, 4, 5. We need to classify each as acute, obtuse, or right using the Converse of the Pythag

1. The problem involves applying the Acute Triangle Inequality Theorem to triangles ABC and JKL. 2. For triangle JKL, the sides are given as J=3, K=4, L=3.

1. The problem asks us to determine which three sticks form a right triangle. According to the Converse of the Pythagorean Theorem, if for three side lengths $a$, $b$, and $c$ (wit

1. We are given that in triangle ABC, $a^2 + b^2 = c^2$, and there is a right triangle DEF with legs $a$ and $b$ and hypotenuse $n$. 2. Since triangle DEF is a right triangle, by t

1. The problem states we have a right triangle with hypotenuse 10, one side 8, and the other side $x$. We need to find $x$. 2. According to the Pythagorean theorem, in a right tria

1. **Problem statement:** Given a circle with center $O$, diameter $AB$, tangent line $ED$ at $C$, angle $\angle A = 36^\circ$, $AO = 12$, and chord $CD = 9$, solve for various ang

1. The problem asks to identify the external secant segment of circle \(\odot M\). An external secant segment is part of a secant line extending outside the circle from the externa

1. The problem describes a rhombus with vertices approximately at $(-5,5)$, $(5,5)$, $(0,10)$, and $(0,0)$ on the coordinate plane. We are asked to find the side length $a$, the he

1. **State the problem:** We need to find the area of a trapezium with two bases of lengths 23.8 cm and 8.5 cm, and a height of 33 cm. 2. **Recall the formula for the area of a tra

1. The problem asks for the area of a triangle with a base of 27.8 metres and a height of 26 metres. 2. Recall the formula for the area of a triangle: $$\text{Area} = \frac{1}{2} \

1. The problem asks for the area of a triangle with base $10$ mm and height $9\frac{3}{10}$ mm (which is $9.3$ mm). 2. The formula for the area of a triangle is $$\text{Area} = \fr

1. **State the problem:** We need to find the area of a trapezoid with the following dimensions: - Top base $b_1 = 1$ km

1. The problem asks for the area of a right triangle with vertical side $2 \frac{7}{10}$ mm and horizontal side $2 \frac{1}{8}$ mm. 2. Convert the mixed numbers to improper fractio

1. The problem presents a pyramid-shaped figure made of rectangles arranged in three levels. 2. The bottom level contains three rectangles; the middle rectangle is labeled with len

1. **State the problem:** Calculate the surface area of the given triangular prism. 2. **Identify the prism's parts:** The prism has two triangular bases and three rectangular face