Too easy to be tough

Geometry Level 3

$ABCD$ is a trapezium in which $ABllCD$ . $CD=30\text{ cm}$ and $AB=50\text{ cm}$ . If $X$ and $Y$ are midpoints of $AD$ and $BC$ then find the ratio of areas $DCYX$ and $ABYX$ .

Constructions okay.

3:5 3:7 7:9 4:5 1:1

2 solutions

Rishabh Sood
Mar 5, 2016

Hint,

Pls post a solution

Chirayu Bhardwaj - 5 years, 3 months ago

Try using mid-point theorem. If you still do not get it hen get back.

Rishabh Sood - 5 years, 3 months ago

no i have get it before only but a question with a solution is much better :)

Chirayu Bhardwaj - 5 years, 3 months ago

@Chirayu Bhardwaj – Hello, Chirayu......I have a simple analytic geometry solution posted above. Glad to help!

tom engelsman - 3 weeks, 3 days ago

Tom Engelsman
May 22, 2021

Quick -n- dirty analytic geometry approach here. Let trapezoid $ABCD$ reside in the first quadrant of the $xy-$ plane such that:

$A(0,0); B(0,h); C(30,h); D(50,0); X(0,h/2); Y(40,h/2)$ .

and $\Large \frac{A_{DCYX}}{A_{ABYX}} = \frac{(1/2)(h/2)(30+40)}{(1/2)(h/2)(40+50)} = \boxed{\frac{7}{9}}.$

Too easy to be tough

2 solutions

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