Question

Solve for x and y

Answer 1

Answer:

x = 2√2

y = 2√6

Step-by-step explanation:

Consider the ratio of the two legs of the two smaller interior right triangles. (refer to attached diagrams for the triangles - I have outlined one in blue and the other in red)

These will be equal since the triangles are similar

shorter leg : longer leg

(blue triangle = red triangle)

⇒ x : 4 = 2 : x

⇒ x/4 = 2/x

⇒ x² = 8

⇒ x = √8

⇒ x = 2√2

Now we have x, we have the two legs of the right triangle with hypotenuse labelled y.

Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse)

⇒ 4² + (2√2)² = y²

⇒ y² = 24

⇒ y = √24

⇒ y = 2√6