Question

Is anyone able to solve this problem?

Answer 1

y = 2
`√(5)`

Explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse )

y² = 2 × (2 + 8) = 2 × 10 = 20 ( take square root of both sides )

y =
`√(20)` =
`√(4(5))` =
`√(4)` ×
`√(5)` = 2
`√(5)`

Answer 2

y = 2√5.

Explanation:

Consider the smallest triangle.

Applying Pythagoras theorem:

y^2 = x^2 + 2^2

The smallest and larger triangle (the one with one side = 8) are similar so we have the proportions :

x/2 = 8/x

---> x^2 = 16

---> x = 4.

Therefore , substituting for x in the first equation:

y^2 = 4^2 + 2^2

---> y^2 = 20

---> y = √20

---> y = 2√5.