6. The hypotenuse of a 45-45- 90 right triangle is 7 cm . Find the lengths of the two legs.

In a 45-45-90 triangle, the legs are equal in length, and they follow the special relationship of the hypotenuse being \( x\sqrt{2} \) where \( x \) is the leg length. Since the hypotenuse is given as 7 cm, we can set up the equation: \( 7 = x\sqrt{2} \). Solving for \( x \), we find that the lengths of the two legs are \( x = \frac{7}{\sqrt{2}} \), which simplifies to approximately 4.95 cm. One fun fact about 45-45-90 triangles: they often show up in architecture and design because of their symmetry! Their equal legs create aesthetically pleasing shapes, particularly in modern minimalist designs. So next time you spot a perfectly squared corner or an elegant triangular roof, remember the hidden math behind its beauty!