Question

Given: AZ = 3 cm, ZC = 2 cm, MC = 5 cm, BM=3 cm. Find: the ratio of areas AXY: AYZ

Answer 1

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 $\bar {XZ} //$ $\bar {BC}$

This is typically and isosceles triangle with a triangle and a parallelogram embedded in it.

So; to solve for XY and YZ; we have

$\frac{\bar {AC}}{\bar {AZ}}$ = $\frac{\bar {BM}}{\bar {XY}}$ = $\frac{\bar {MC}}{\bar {YZ}}$

$\frac{\bar {5}}{\bar {3}} =\frac{\bar {3}}{\bar {XY}}=\frac{\bar {5}}{\bar {YZ}}$

Let's first solve for XY :

= $\frac{\bar {5}}{\bar {3}} =\frac{\bar {3}}{\bar {XY}}$

3 × 3 = 5(XY)

9 = 5(XY)

XY = $\frac{\bar {9}}{\bar {5}}$

XY  = 1.8

From XY = 1.8

we have:

$\frac{3}{XY}=\frac{5}{YZ}$

$\frac{3}{1.8}=\frac{5}{YZ}$

3(YZ) =5 × 1.8

YZ = $\frac{5*1.8}{3}$

YZ = 3

∴ XY: YZ

= 1.8 : 3

Answer 2

Answer:

Given: AZ = 3 cm, ZC = 2 cm, MC = 5 cm, BM=3 cm. Find:

the ratio of areas XY: YZ

Step-by-step explanation: