Question

the length oh hypotenuse of right triangle exceeds its base by 4cm and altitude exceeds its base by 2cm find hypotenus

Answer 1

Answer:

Let the length of base be y

Hypotenuse = y + 4

Altitude = y + 2

By Pythagoras Theorem:-

(B)² + (A)² = (H)²

(y)² + (y+2)² = (y+4)²

y² + y² + 4y + 4 = y² + 8y + 16

2y² + 4y + 4 = y² + 8y + 16

2y² + 4y + 4 - y² - 8y = 16

y² - 4y + 4 = 16

y² - 4y = 16 - 4

y² - 4y = 12 — (i)

Now we factorise the term:-

y² - 4y = 12

y² - 4y - 12 = 0

y² - 6y + 2y - 12 = 0

y(y-6) + 2(y-6) = 0

(y+2)(y-6) = 0

⇒ y = 6 OR -2

But since the base of a triangle can’t be negative, we will take the value of y as 6.

Hypotenuse = y + 4

= 6 + 4

= 10 cm

Altitude = y + 2

= 6 + 2

= 8 cm

Base = y

= 6 cm

VERIFY:-

(B)² + (A)² = (H)²

(6)² + (8)² = (10)²

36 + 64 = 100

100 = 100

LHS = RHS

Hence, verified

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