A trapezoid was broken into two congruent triangles and a rectangle. A trapezoid is broken into 2 triangles and 1 rectangle. The triangles both have a base of 3 centimeters and a height of 12 centimeters. The rectangle has a height of 12 centimeters and a width of 14 centimeters. What is the base length, b, of one of the triangles? 3 cm 4 cm 6 cm 7 cm

complete question:

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base of the triangles = 3 cm

Step-by-step explanation:

The trapezoid was broken into 2 congruent triangles and a rectangle. The 2 triangle have a height of 12 cm . The rectangle has a height of 12 cm and width of 14 cm .

The base length of the triangle can be computed as follows.

Note a congruent triangle have exactly the same three sides and exactly the same three angles.

area of a triangle = 1/2 × base × height

From the area of the trapezoid one can calculate the sides of the triangle.

area of the trapezoid = 1/2 × (a + b)h

where

a = top side

b = base side

h = height

area of the trapezoid = 1/2 × (a + b)h

area of the trapezoid = 1/2 × (14 + 20)12

area of the trapezoid = 1/2 × 34 × 12

area of the trapezoid = 34 × 6

area of the trapezoid = 204 cm²

204 = area of the triangles + area of the rectangle

204 =2 (1/2bh) + lw

where

b = base of triangle

h = height of triangle

l = length of rectangle

w = width of rectangle

204 = bh + (14 × 12)

204 = 12b + 168

12b = 204 - 168

12b = 36

divide both sides by 12

b = 36/12

b = 3 cm

base of the triangles = 3 cm

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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