Question

the length of the hypotenuse of right triangle exceeds the base by 2
cm and exceeds twice the length of altitude by 5 cm. the length altitude of triangle will be

Answer 1

Answer:

Altitude = 8cm

Step-by-step explanation:

Let the altitude of triangle be x cm.

Hypotenuse of triangle = 2x + 1

Base of triangle = 2x - 1.

According to the Question,

Using Pythagoras theorem,

⇒ (2x + 1)² = x² + (2x - 1)²

⇒ 4x² + 1 + 4x = x² + 4x² + 1 - 4x

⇒ x² - 8x = 0

⇒ x(x - 8) = 0

⇒ x = 0, 8 (Neglecting 0)

⇒ x = 8 cm

Altitude of triangle = x = 8 cm

Hypotenuse of triangle = 2x + 1 = 2(8) + 1 = 16 + 1 = 17 cm

Base of triangle = 2x - 1 = 2(18) - 1 = 16 - 1 = 15 cm.