Answer:
w = 10√2
y = 20
Explanation:
Sum of interior angles of a triangle = 180°
Therefore, the triangle on the left (with side length 10) is a right triangle,
since 180° - 45°- 45° = 90°
As this triangle is also an isosceles triangle (since it has 2 equal angles), then it will have 2 sides of the same length.
So the legs of the right triangle are both 10 units.
Using Pythagoras' Theorem to calculate the hypotenuse of this triangle:
⇒ 10² + 10² = c²
⇒ 200 = c²
⇒ c = √200
⇒ c = 10√2
The triangle with side w and base y is also isosceles triangle with base angles of 45°.
Therefore, the sides are equal in length.
So w = hypotenuse of the left triangle = 10√2
We know that the horizontal distance between the left base vertex and the top vertex of this triangle is 10, therefore y = 10 + 10 = 20