Question

Find Y and explain how

Answer 1

Let us assume, Length of Unknown Side of the Whole Triangle be : p

As the Whole Triangle is a Right Angled Triangle :

⇒ p² + 6² = (y + 4)²

⇒ p² = (y + 4)² - 36

Now We can Notice that the Whole Right Angled Triangle is Divided into Two Right Angled Triangles (Smaller One on the Top and Larger One at the Bottom)

Now Consider Smaller Right Angled Triangle :

Let the Unknown Side of the Smaller Right Angled Triangle be : z

⇒ z² + 4² = 6²

⇒ z² + 16 = 36

⇒ z² = 20

Now Consider the Larger Right Angled Triangle at the Bottom :

⇒ y² + z² = p²

⇒ y² + 20 = (y + 4)² - 36

⇒ y² = y² + 16 + 8y - 56

⇒ 8y - 40 = 0

⇒ 8y = 40

⇒ y = 5

Option b is the Answer