Question

Find the value of x and the value of y

Answer 1

Answer:

A

Step-by-step explanation:

Since DE is parallel to AB and intersects the other 2 sides, it divides those sides proportionally, that is

$\frac{BE}{EC}$ = $\frac{AD}{DC}$

Note that AD = 33 - 22 = 11

Substitute values into the ratio

$\frac{x}{16}$ = $\frac{11}{22}$ = $\frac{1}{2}$ ( cross- multiply )

2x = 16 ( divide both sides by 2 )

x = 8

To find y use similar triangles

Δ ABC is similar to Δ DEC, thus ratios of corresponding sides are equal

$\frac{AB}{DE}$ = $\frac{AC}{DC}$, substitute values

$\frac{18}{y}$ = $\frac{33}{22}$ = $\frac{3}{2}$ ( cross- multiply )

3y = 36 ( divide both sides by 3 )

y = 12

Thus y = 12, x = 8 → A

Answer 2

Answer:

y = 15.1 , x = 11.7

Step-by-step explanation:

Using pythagoras theorem

Hypothenus ^2 = opposite^2+adjacent ^2

33^2= 18^2+(16+Using pythagoras theorem

Hypothenus ^2 = opposite^2+adjacent ^2

22^2= 16^2+y^2

484= 256+y^2

484-256 = y^2 = 228

y = sqrt 228 = 15.0996688705= 15.1

Using pythagoras theorem

Hypothenus ^2 = opposite^2+adjacent ^2

33^2= 18^2+(16+x)^2

1089= 324+(16+x)^2

1089-324= (16+x)^2

765 = (16+x)^2

16 + x = sqrt 765

16 + x = 27.6586333719

x = 27.6586333719 -16 = 11.6586333719 = 11.7