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Triangle ABC and triangle DEF are congruent, isosceles right triangles. The square
inscribed in triangle ABC has an area of 15 square centimeters. What is the area of the square inscribed in
triangle DEF? Express your answer as a common fraction. Please show your work.

 

 Oct 23, 2022
 #1
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The area of the square inscribed in triangle DEF is 25/2.

 Oct 23, 2022
 #2
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The sidelength of the square inscribed in ABC has to be half of BC.

 

The sidelength of the square inscribed in DEF has to be a third of DF.

 

The ratio of BC:DF is 1:square root of 2

The ratio of 1/2:1/3 is 3:2

The ratio of the sidelength of the square inscribed in ABC to that of the square inscribed in DEF is 3:2 times the square root of 2.

Therefore, the ratio of their areas is 9:8.

 15 x 8/9 = 40/3

 Oct 23, 2022

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