jmc

Question

In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle ABCD. What is the length in centimeters of segment EF? Express your answer in simplest radical form. FIGURE

Accepted Answer

The area of the rectangle is (6)(8)=48, so the area of triangle DEF is 48/4 =12. Since DE=DF, the area of DEF is (DE)(DF)/2 = DE^2/2, so DE^2/2 = 12. Therefore, DE^2 = 24. From the Pythagorean Theorem, we have EF^2 = DE^2 +DF^2 = 24+24=48, so EF =48 = 43.