Triangle GHK has an area of m square units. If the height of the triangle is increased to five times the current height, and the length of the base increased to four times the current length, what will be the area of the larger triangle?

20m square units

Step-by-step explanation:

The area of a traingle  = bh/2 Equation 1

Where b = lenght of the base, h = heigt of the triangle.

From the question,

The area of triangle GHK = m square units., let the base and the heigth of the triangle be x and y respectively

Therefore,

b = x, h = y

Substitute these values into equation 1

m = xy/2 Equation 2

If the height of the triangle increase to five times the current height, and the length of the base increase to four times the current length.

Therefore,

height of the larger triangle = 5y, base of the larger triangle = 4x

Substitute these values into equation 1

Area of the larger triangle = (5y×4x)/2

Area of the larger triangle = 20xy/2 Equation 3

Substitute equation 2 into equation 3

Area of the new triangle = 20m square units.

linear pair postulates