Question

Find the area of triangle if the altitude of a right triangle is 34 cm less than its base with the hypotenuse 50 cm.

solve by process ​

Answer 1

Step-by-step explanation:

"Let the base of the right triangle = x.

Altitude = x-7

Hypotenuse = 13 cm

The quadratic representation is 13^2 = x^2 +(x-7)^2.

The solution is 169 = x^2 + x^2–14x+49, or

120 = 2x^2–14x or

x^2–7x-60 = 0

(x-12)(x+5) = 0. x= -5 has no relevance, here.

Hence x = 12 cm and the altitude is 5 cm."

Answer 2

Answer:

Let x be the base of the triangle, then the altitude will be (x−7).

By Pythagoras theorem,

x

2

+(x−7)

2

=(13)

2

2x

2

−14x+49−169=0

2x

2

−14x−120=0

x

2

−7x−60=0

x

2

−12x+5x−60=0

(x−12)(x+5)=0

x=12,x=−5

Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and the altitude of the triangle will be 12−7=5cm.