📐 geometry

1. The problem states we have a right-angled triangle with sides 9 m, $\sqrt{4819}$ m, and a hypotenuse of 70 m. We need to find the gradient of the hypotenuse (70 m line) as a per

1. You asked to draw the geometry, but this problem does not specify any particular geometric figure or equation to graph. 2. Please provide the specific geometric shape, equation,

1. Problem statement: You are given a line segment AB of length 6 cm. 2. Mark a point P near the midpoint of AB using a ruler.

1. **Problem:** Muthu put a 5.4 m ladder against Mandy's window 5.2 m above the ground. Find the distance from the base of the ladder to the wall. Step 1: Identify that this forms

1. **Problem 1a: Intersecting Tangent and Secant Segments** We have a circle with center $R$, a tangent segment $MT$ touching the circle at point $T$, and a secant segment $PT$ int

1. **State the problem:** We need to find the height $h$ of a cylindrical container with volume $769691$ cm³ and radius $r=7$ cm. 2. **Recall the volume formula for a cylinder:**

1. **Problem Statement:** We have a concrete beam in the shape of a rectangular prism resting on two closed cylinders (pillars). We need to find:

1. The problem asks to classify sequences of transformations applied to polygon I to see if it maps congruently onto polygon II. Both polygons are on coordinate plane quadrants: I

1. The problem asks us to identify which shapes are similar to shape A, a purple diamond centered at (-5, -2). 2. Similar shapes have the same shape but can differ in size, orienta

1. The problem states that square ABCD is on the coordinate plane with vertices: A(-4, -1), B(-2, -1), D(-4, -4), and C(-2, -4). 2. Paige first dilates this square by a scale facto

1. The problem asks for the area of a shape where the width is given as $x$ cm. 2. To find the area, we need to know the length and the width of the shape.

1. **Stating the problem:** We have a square park with a side length of 40 meters. A flower bed 3 meters wide runs along all four sides of the park. We need to find the area of the

1. Problem: Find unknown angle $a$ in a circle with a central angle of 118° opposite to $a$. Step 1: Recall the inscribed angle theorem: an inscribed angle is half the measure of i

1. **State the problem:** We have a right triangle with sides 4 units, 5 units, and an unknown side length $x$. We want to find the difference between the possible values of $x$ th

1. Stating the problem: We have an acute triangle with the longest side measuring 30 inches and the other two sides congruent but unknown in length. 2. Let the length of each congr

1. **Problem:** Given a circle with a central angle of 118° and inscribed angle $a$ opposite the chord forming the angle, find $a$. - Step 1: Recall the circle theorem that states

1. **State the problem:** We need to determine the classification of a triangle with side lengths 6 cm, 10 cm, and 12 cm. 2. **Recall the triangle inequalities and types by angles:

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