Correct answers only !
a student sketched some art on an 8.5 inch x 11 inch piece of paper. he wants to resize it to fit an 5 inch x 7 inch frame (as shown below)
what is the value of x? (hint: like step #1 of the example in class)
a. x = 5
b. x = 6
c. x = 5.41
d. x = 7

x = 5.41

Step-by-step explanation:

The picture is originally 11 inches wide by 8.5 inches tall.  It gets scaled down to a new width of 7 inches.  We need to find the new height.  To do this, we write a proportion:

8.5 / 11 = x / 7

Cross multiply:

11x = 59.5

Divide:

x = 5.41

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)