Question

The area of triangle is 24 cm2 .if its height is 2 cm longer than its base find the base of the triangle

Answer 1

Let the base of the triangle be x cm
Therefore height of the triangle is (x+2) cm
Area = 24 cm^2
1/2 x(x + 2) = 24
=> (x^2) + 2x - 48 = 0
=> (x^2) + 8x - 6x - 48 = 0
=> x(x + 8) - 6(x + 8) = 0
=> (x - 6)(x + 8) =0
Solution
Either x = -8
or x = 6
As height of the triangle cannot be negative
Therefore height = 6 cm
And base =6 - 2 = 4 cm
Hope it helps you

Answer 2

Given :

• The Base and Height of the triangle are in the ratio of 2:3. And, area of the triangle is 180 cm²

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To Find :

• The Base and Height of triangle.

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Solution :

Let the Base and Height of the triangle be 2x and 3x respectively.

As we know that,

★ Area of triangle = 1/2 × (Base) × (Height)

→ 108 = 1/2 × (2x) × (3x)

→ 108 = 3x²

→ x² = 108/3

→ x² = 36

→ x = √36

→ x = 6

Hence,

➠ Base of triangle, 2x = 2 × (6) = 12 cm

➠ Height of triangle, 3x = 3 × (6) = 18 cm