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AMC 10 USA Math Olympiad

2D Geometry AMC 8, 2019 Problem 2

Try this beautiful problem from AMC 10. It involves geometry of triangles. We provide sequential hints so that you can try the problem.

What are we learning ?

Competency in Focus: 2D Geometry (Area of Rectangle)

This problem from American Mathematics contest (AMC 8, 2019) is based on calculation of area of  Rectangle .

First look at the knowledge graph

knowledge graph of area of rectangle

Next understand the problem

Three identical rectangles are put together to form rectangle $ABCD$, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle $ABCD$?  
Source of the problem
American Mathematical Contest 2019, AMC 8  Problem 2
Key Competency

2D Geometry (Area of Rectangle)

Difficulty Level
3/10
Suggested Book
Challenges and Thrills in Pre College Mathematics  

Start with hints 

Do you really need a hint? Try it first!
The length of the smaller side of each rectangle is given 5 feet. So using the diagram we can find  that the larger side of the small rectangle is 2 times the length of the smaller side.
So find the longer side which is 5*2 = 10 feet.
 the area of the identical rectangles is 5*10 = 50 square feet
  Thus at end we have 3 identical rectangles formed a bigger rectangle……Try to solve …   50*3 = 150 square feet 

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