Question

Triangle ABC above is isosceles with AB=AC and BC=48. The ratio of DE to DF is 5 : 7. What is the length of DC?

Answer 1

The triangle ABC is an isosceles with AB=AC.

BC=48

Now given that

DE:DF=5:7.

Since DE is perpendicular to AB and DF is perpendicular to AC, therefore,

BD:DC=5:7

It happens because as DE:DF=5:7, the ratio of the area of the two reight angle triangles is also 5:7.

So, their base must be in the same ration.

Now, two sides are in same ratio, by default, their third sides i.e., BD and DC have the ratio 5:

Since, BC=48, therefore,

$\begin{gathered} DC=\frac{7}{12}\times48 \\ =28 \end{gathered}$

Hence, the correct option is (D).