Question

The area of a right triangle is 30 sq. m.
Determine its base, if height exceeds the base
by 7 m

Answer 1

Answer:

Step-by-step explanation:

let base be X

height exceeds  the base by 7

height is    X + 7

AREA = [1/2] bh  =30

      [1/2] [X] [X+7] =30

  X[X+7] =60 =5[12]

x[x+7] = 5 [5+7]  

clearly   x = 5

base   5 m

height  12 m

you may find from  x^2 +7x -60 =0

but here I use another idea

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 height of a triangle is 7 m greater than its base.

The area of the triangle is 30 m²

So, let the base of triangle = x

So, height of triangle will be = (x +7)

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,

$Area = \frac{1}{2}\times x\times (x+7)\\30 = \frac{1}{2}\times x\times (x+7)\\60 = x^2+7x\\=>x^2+7x-60 = 0\\=>x^2+12x-5x-60=0\\=>x(x+12)-5(x+12)=0\\=>(x-5)(x+12)=0\\=>x = -12, 5$

As x can't be negative,

So, we will consider the value of x as 5

So, base of triangle will be 5 m

So, height of triangle will be 12 m