Question

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.​

Answer 1

Answer:

umm

Step-by-step explanation:

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Answer 2

S O L U T I O N :

Let,

• The base of a right Δ is R cm.
• The altitude of a right Δ be (R - 7) cm.
• The hypotenuse of a right Δ be 13 cm.

According to the Pythagoras theorem,

Base ² + Altitude² = Hypotenuse²

[ Put the values ]

⇒ R² + (R - 7)² = 13²

⇒ R² + R² + 49 - 14R = 169

⇒ 2R² - 14R - 120 = 0

⇒ R² - 7R - 60 = 0

⇒ R² - 12R + 5R - 60 = 0

⇒ R(R - 12) + 5(R - 12) = 0

⇒ (R - 12) (R + 5) = 0

⇒ R = 12 , -5

[ Note :- Ignoring negative term ]

⇒ R = 12 cm

Therefore,

• The base of a right Δ is 12cm.
• The altitude of a right Δ is 5cm.