A geometry problem by A Former Brilliant Member

Geometry Level 3

A quadrilateral is divided into four areas as shown. The area of the yellow portion is 427 square meters. The area of the green portion is 825 square meters. Which of the following represents the best approximation for the area of the blue portion?

note: line XY is parallel to line VZ

1700 square meters 1500 square meters 1600 square meters 1400 square meters

1 solution

Maria Kozlowska
Dec 26, 2016

Let $VY$ and $XZ$ intersect at point $O$ .

$\frac{\triangle VOX}{\triangle XYO }=\frac{825}{427}=\frac{VO}{OY}$

Triangles $XYO$ and $VOZ$ have all their angles equal therefore are similar. Their corresponding sides are in the same ratio $\frac{825}{427}$ and their areas are in the ratio $(\frac{825}{427})^2$ . $\triangle VOZ=( \frac{VO}{OY} )^2 \triangle XYO= (\frac{825 }{427})^2 \times 427= \frac{680625} {427} \approx 1593.97$

A geometry problem by A Former Brilliant Member

1 solution

0 pending reports