Question

the altitude of an triangle is 6 cm is greater than its base if the area is 108cm cube find the breadth and height​

Answer 1

Your question needs a correction.

Since unit of area can't contain cube, correct question : the altitude of an triangle is 6 cm is greater than its base if the area is 108cm square find the breadth and height.

Solution : -

Let the base of triangle be of length a cm.

As given in the question, altitude of the triangle is 6 cm more than its base, a cm, length of its altitude should be 6 cm more than a cm i.e. a cm + 6 cm, thus altitude of the triangle should be ( a + 6 cm ) if length of base is a cm.

It is given that the area of the triangle is 108 cm^2 , and from the properties of triangle we know that the area of any triangle is half of the product of its base and altitude.

Thus,

= > Area of the triangle = 108 cm^2

= > 1 / 2 x a cm x ( a + 6 ) cm = 108 cm^2

= > a( a + 6 ) = 2 x 108

= > a^2 + 6a = 216

= > a^2 + 6a - 216 = 0

= > a^2 + ( 18 - 12 )a - 216 = 0

= > a^2 + 18a - 12a - 216 = 0

= > a( a + 18 ) - 12( a + 18 ) = 0

= > ( a + 18 )( a - 12 ) = 0

= > a = - 18 or 12.

Thus,

length of base of the triangle should be 12 cm, since it can't be negative, it can't be - 18 cm.

And, length of altitude of the triangle is 12 cm + 6 cm = 18 cm.

Answer 2

Correct question: The Altitude of an triangle is 6 cm greater than its base. If the area is 108 cm², find the base and height.

Answer:

Base = 12 cm

Altitude = 18 cm

Step-by-step explanation:

Let the base of triangle be x cm, then as it is given that altitude of the triangle is 6 cm more than its base, therefore altitude of triangle be ( x + 6 ) cm.

Now, find the area of triangle,

Area of triangle = 108 cm²

⇒ $\dfrac{1}{2}$ * base * height = 108

⇒  $\dfrac{1}{2}$ * x * (x + 6) = 108

⇒  $\dfrac{x(x+6)}{2}$ = 108

⇒ x² + 6x = 216

⇒ x² + 6x - 216 = 0

⇒ x² + 18x - 12x - 216 = 0

⇒ x ( x + 18 ) - 12 ( x + 18 ) = 0

⇒ ( x + 18 ) ( x - 12 ) = 0

⇒ x = - 18 or x = 12

Since, base cannot be negative, taking the positive value of x, we have ;

Base = x = 12 cm

Altitude = x + 6 = 18 cm

Hence, the base and altitude of triangle is 12 cm and 18 cm.