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142.5 in^2

Step-by-step explanation:

First, find the area of the rectangle

19*10= 190

Now find the area of the triangle

A=1/2bh

A=1/2(19)(10-5)

A=47.5

Since we need the shaded region, subtract the triangle area from the rectangle area

190-47.5=142.5

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.

the answer is c.

step-by-step explanation: