We are given that Grace wants to decorate the gable of the house, which is an isoscelesright triangle, and we are asked to find how many feet of lights Grace will need to cover the gable. Let's notice that the height of the gable divides it into two 45^(∘)-45^(∘)-90^(∘) triangles.
Recall that in 45^(∘)-45^(∘)-90^(∘) triangles the legs are congruent and the hypotenuse is sqrt(2) times the length of a leg. Using this information, we can complete the picture with all the missing measures.
Now we will add the appropriate lengths of the gable below the roof line.
8 sqrt(2)+ 8 sqrt(2)=16sqrt(2)≈22.6
Grace will need approximately 22.6 feet of lights to cover the gable below the roof.
