Area of Triangle ABC: Find Solution

[youngstudent16]

Homework Statement

In triangle ABC, ∠C=90∘. Let D, E, F be points on sides BC, AC, AB, respectively, so that quadrilateral CDFE is a rectangle. If [BDF]=7 and [AEF]=28, then find [ABC].

Homework Equations

Area of a rectangle, and triangle. Also can cut up the rectangle into some triangles

The Attempt at a Solution

I'm not sure what [ABC] is. Is it asking for the perimeter or the area? I'm assuming area so I know the 1/2bh=28 for one and 7 for the other. I have to figure out some relation between those and the rectangle to get the sides of the rectangle in order to find the total area.

 

[youngstudent16]

OH I figured it out with similar triangles between the two known areas getting 63 for the final answer

Drawing helps

 

[feyn_stein17]

[ABC] is the area of the triangle. Try finding the area of the rectangle inside the triangle. Once you do that, you can add it together to the areas of the small triangles to get the total area of [ABC].