Inconvenient Length Measures

Geometry Level 2

Susan cuts out a rectangle from the corner of a right triangle.

While she doesn't know the dimensions of the rectangle, she does know the lengths of the remaining sides on the triangle, which are 2 and 4,

What is the area of the rectangle?

6 8 4 Cannot be determined

1 solution

Ayush G Rai
Nov 13, 2016

Given $AF=2$ and $CE=4.$ Let $BF=DE=x$ and $FD=BE=y.$
We observe that $FD || BC,$ $\angle AFD=\angle DEC=90^\circ$ and $\angle ADF=\angle ACB.$ So $\triangle AFD\sim\triangle DEC.$
By using similarity properties, $\dfrac{AF}{DE}=\dfrac{FD}{EC}\Rightarrow \dfrac{2}{y}=\dfrac{x}{4}\Rightarrow xy=8.$
Since the area of rectangle $=width\times breadth=xy=\boxed{8}.$

Tg(acb)=x/4=2/y

Xy=8

Kris Hauchecorne - 4 years, 7 months ago

thanks i have edited my solution.

Ayush G Rai - 4 years, 7 months ago

Inconvenient Length Measures

1 solution

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