The area of a right angled triangle is 165 m2. Determine its base and altitude if the latter exceeds the former by 7 m.
Let the base of the triangle be ‘a’.
Given, altitude exceeds the base by 7 m.
⇒ Altitude = a + 7 m
Area of a right angled triangle = 1/2 × base × height
⇒ 1/2 × a(a + 7) = 165
⇒ a2 + 7a – 330 = 0
⇒ a2 + 22a – 15a – 330 = 0
⇒ a(a + 22) – 15(a + 22) = 0
⇒ (a – 15)(a + 22) = 0
⇒ a = 15 m
Altitude = 15 + 7 = 22 m