Triangle with equal heights

Geometry Level pending

Lines m m and n n are parallel. The area of △ A B C \triangle ABC is 17.5 17.5 and △ X Y Z \triangle XYZ is 35 35 . If the length of B C BC is 5 5 , find the length of Y Z YZ .


The answer is 10.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Recall that the areas of triangles with equal altitudes are proportional to the bases of the triangles. We have

Y Z B C = A X Y Z A A B C \dfrac{YZ}{BC}=\dfrac{A_{XYZ}}{A_{ABC}}

Y Z 5 = 35 17.5 \dfrac{YZ}{5}=\dfrac{35}{17.5}

Y Z = 10 \boxed{YZ=10}

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