Question

the altitude of a triangle is 6 cm more than its base if its area is 108 CM² find the base and height of the triangle​

Answer 1

Answer :

• Base of triangle is 12cm and height of triangle is 18cm

Given :

• The altitude of a triangle is 6cm more than its base
• Area is 108 cm²

To find :

• Base and height of the triangle

Solution :

• Let the base of triangle be x

Given that, the altitude of a triangle is 6cm more than its base then,

• (x + 6)

Area is 108cm²

As we know that,

• Area of triangle = 1/2 × b × h

Where , b is base and h is height (Altitude)

》108 = 1/2 × x × (x + 6)

》x² + 6x = 108 × 2

》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

So, base can't be negative then take the x value (positive)

• Base = x = 12cm
• Altitude = x + 6 = 12 - 6 = 18cm

Hence,base of triangle is 12cm and height of triangle is 18cm