Question

The base of a triangle is 6m greater than its height. If the area of the triangle is 108m². Determine the dimensions of the base and height.

Answer 1

Answer:

The base of triangle is 12cm

Step-by-step explanation:

Let the base of the triangle be x. 

It is given that the altitude of the triangle is 6 cm greater than its base, therefore, the altitude of the triangle is (x+6). 

It is also given that the area of the triangle is 108 cm2.

We know that the area of the triangle is A=21×b×a, therefore,

108=21(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−12)=0,(x+18)=0⇒x=12,x=−18

Since the length of the triangle cannot be negative thus, x=12.

Hence, the base of the triangle is 12 cm.

Answer 2

In context to question asked,

We have to determine the value of base and height of the triangle.

As per question,

We have,

The base of a triangle is 6m greater than its height.

The area of the triangle is 108m²

So, let the height of triangle = x

So, base of triangle will be = (x +6)

As we know that,

Area of triangle can be calculated by using formula,

$Area = \frac{1}{2}\times b \times h$

So, for determining the value of area, we will put the value of base and height,

Thus we will get,

$Area = \frac{1}{2}\times x\times (x+6)\\=>108 = \frac{1}{2} \times x \times (x+6)\\=>x(x+6) = 108\times 2\\=>x^2+6x = 216\\=>x^2+6x -216 = 0\\=>x^2+18x-12x-216=0\\=>x(x+18)-12(x+18) = 0\\=>(x-12)(x+18) = 0\\=>x = 12, -18$

As x can't be negative,

So, we will consider the value of x as 12

So, height of triangle will be 12 m

So, base of triangle will be 18 m