The triangles shown below must be congruent. M
40°
40°
12
12
O A. True
O B. False

True

The statement is true because :

Both these triangles are Congruent to each under the ASA congruence postulate . We say this because :

1) The two angles in both the triangles which are each other's corresponding part are equal ( 40° = 40° and 50° =50° )

2) There is one common side which is 12 . As both of the common sides are equal , these triangles are said to be congruent to each other .

Let s be the measure of the measure of the sides of the square such that its area is s². From the conditions above, the length of the rectangle is s + 5 and its width is 0.5s. The area of the rectangle is (s+5)(0.5s)
                             s² = (s + 5)(0.5s) 
The value of s is 5. Thus the dimension of the rectangle in w x h is 2.5 x 10.