Question

Determine x, y, and z in the diagram. Assume the segment in the middle of the triangle is the midsegment of the triangle.

drag and drop

X=
Y=
Z=

Answer 1

Check the picture below.

now, the tiny triangle with the midsegment and the large containing triangle are both similar triangles by AA, so that means

`\cfrac{z-16}{y}=\cfrac{z}{14}\implies \cfrac{z-16}{7}=\cfrac{z}{14}\implies 14z-224=7z \\\\\\ 7z-224=0\implies 7z=224\implies z=\cfrac{224}{7}\implies \boxed{z=32} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{21}{y}=\cfrac{x+21}{14}\implies \cfrac{21}{7}=\cfrac{x+21}{14}\implies 294=7x+147 \\\\\\ 147=7x\implies \cfrac{147}{7}=x\implies \boxed{21=x}`