Here is the correct question.
Given: AZ = 3 cm, ZC = 2 cm, MC = 5 cm, BM=3 cm. Find:
the ratio of areas XY: YZ
Answer:
XY : YZ = 1.8 : 3
Step-by-step explanation
From the diagram below:
Line XZ is parallel to Line BC
i.e [tex]\bar {XZ} //[/tex] [tex]\bar {BC}[/tex]
This is typically and isosceles triangle with a triangle and a parallelogram embedded in it.
So; to solve for XY and YZ; we have
[tex]\frac{\bar {AC}}{\bar {AZ}}[/tex] = [tex]\frac{\bar {BM}}{\bar {XY}}[/tex] = [tex]\frac{\bar {MC}}{\bar {YZ}}[/tex]
[tex]\frac{\bar {5}}{\bar {3}} =\frac{\bar {3}}{\bar {XY}}=\frac{\bar {5}}{\bar {YZ}}[/tex]
Let's first solve for XY :
= [tex]\frac{\bar {5}}{\bar {3}} =\frac{\bar {3}}{\bar {XY}}[/tex]
3 × 3 = 5(XY)
9 = 5(XY)
XY = [tex]\frac{\bar {9}}{\bar {5}}[/tex]
XY = 1.8
From XY = 1.8
we have:
[tex]\frac{3}{XY}=\frac{5}{YZ}[/tex]
[tex]\frac{3}{1.8}=\frac{5}{YZ}[/tex]
3(YZ) =5 × 1.8
YZ = [tex]\frac{5*1.8}{3}[/tex]
YZ = 3
∴ XY: YZ
= 1.8 : 3
