Triangle A B C is shown. Angle A B C is a right angle. An altitude is drawn from point B to point D on side A C to form a right angle. The length of A D is x, the length of D C is 4 x, and the length of B D is 10. What is the value of x? 2 units 3 units 5 units 8 units

b.

step-by-step explanation:

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3

the answer is 0.8in^2

hope you get it down chief.

• before the lesson, students attempt the assessment task individually. you then review students’

solutions and formulate questions that will them improve their work.

• during the lesson, students work collaboratively in pairs or threes, plotting graphs, completing

tables of values and deducing equations. then, based on the number of common solutions,

students link these representations.

• in a follow-up lesson, students receive your comments on the assessment task and use these to

attempt the similar task, approaching it with insights gained from the lesson.