📐 geometry

1. The problem states we have a right triangle with legs 12 and 16, and hypotenuse $x$. 2. By the Pythagorean theorem, $x^2 = 12^2 + 16^2$.

1. The problem is to find the value of $x$ in a right triangle where the vertical side is 2, the horizontal side is 10, and $x$ is the hypotenuse. 2. According to the Pythagorean t

1. The problem states we have a right triangle with legs of lengths 5 and 12, and the hypotenuse labeled as $x$. 2. By the Pythagorean theorem, in a right triangle, the square of t

1. **State the problem:** We are given two angles, \(\angle A = 6x - 35^\circ\) and \(\angle B = 3x + 53^\circ\), formed by two parallel lines crossed by a transversal. We need to

1. The problem gives two angles formed by a transversal cutting two parallel lines: \(\angle A = 6x + 18^\circ\) and \(\angle B = x + 93^\circ\). These angles are interior angles o

1. The problem gives two angles \(\angle A = 6x - 18^\circ\) and \(\angle B = 14x + 38^\circ\) formed by a transversal intersecting two parallel lines. 2. Since \(\angle A\) and \(

1. **Exercice 1** Énoncé : Dans un triangle avec BC = 6, AE = 2, AB = 5, et (EF) // (BC).

1. The problem is to translate rhombus CDEF 4 units left and 13 units down on the coordinate plane. 2. The original coordinates are:

1. The problem asks us to translate the polygon 5 units to the right. 2. Translation 5 units right means adding 5 to the x-coordinate of each vertex, while the y-coordinate remains

1. **State the problem:** We need to find the coordinates of the vertices E', F', G', and H' after a 180° counterclockwise rotation around the origin. 2. **Recall the rotation rule

1. **State the problem:** We have a right pyramid with a regular pentagonal base of side length 20 cm, vertical height 80 cm, and all slant edges equal. We need to find the total s

1. **State the problem:** We need to find the distance between points A(3, -1) and B(-1, 4). 2. **Recall the distance formula:** The distance $d$ between two points $(x_1, y_1)$ an

1. The problem involves verifying the angle values in a diamond shape inscribed in a circle, with given angles 48°, 48°, 96°, and 84°. 2. First, check the sum of angles in the diam

1. **Problem (a):** Find $x$ and $y$ in the triangle with angles $44^\circ$, $y$, and an exterior angle $68^\circ$ adjacent to $x$. 2. The exterior angle $68^\circ$ equals the sum

1. **State the problem:** We have two similar tanks with capacities 1,000,000 litres and 512,000 litres respectively. The smaller tank has a surface area of 1200 m². We need to fin

1. **Problem statement:** Given cyclic quadrilateral ABCD with center O, AB and CD extended meet at E, DC=BC, and \(\angle BCE=48^\circ\). Find angles \(\angle BAD\), \(\angle BDC\

1. **State the problem:** We have a regular pentagon with an inscribed circle (incircle) of radius $r=5$ cm. We need to find the area of the pentagon outside the circle, i.e., $\te

1. **State the problem:** We have a sector of a circle with area 550 cm². This sector is curved to form an open cone with radius 7 cm. We need to find the height of the cone. 2. **

1. **State the problem:** We need to find the perpendicular bisectors of the lines $x+y=0$ and $x-y=0$, which intersect at the origin, and analyze the right triangle with vertices

1. **State the problem:** We are given two lines $x+y=0$ and $x-y=0$ intersecting at the origin, which is the circumcenter of a right triangle with vertex $A(5,7)$. 2. **Identify t

1. সমস্যাটি হলো: একটি রম্বসের দুইটি কর্ণ ৭ সেমি এবং ৪ সেমি, এবং একটি কোণ ৬০ ডিগ্রী দেওয়া আছে। রম্বসটির ক্ষেত্রফল নির্ণয় করতে হবে। 2. রম্বসের ক্ষেত্রফল নির্ণয়ের সূত্র হলো: $$\tex