Question

The height of a triangle is 6 more than the base. The area is 216m^2. Find the base and the height of the triangle.

Answer 1

Answer:

The length of base is 18 m and height is 24 m .

Step-by-step explanation:

Let the base of ∆ be x .

then the height be ( x + 6 )

A/q

Area of ∆ = 216 m^2

=> 1/2 × b × h = 216

=> 1/2 × x × ( x + 6 ) = 216

=> 1/2 ×( x^2 + 6x ) = 216

=> x^2 + 6x = 216 × 2

=> x^2 + 6x = 432

=> x^2 + 6x - 432 = 0

=> x^2 + 24x - 18x - 432 = 0

=> x ( x + 24 ) - 18 ( x + 24 ) = 0

=> ( x + 24 ) ( x - 18 ) = 0

here , x = -24 or 18

Since , the length of base of ∆ can't be negative .

so, x = 18 = base

and

height = x + 6

= 18 + 6

= 24

Hence ,

The length of base is 18 m and height is 24 m .

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