Answer:
x=3
Step-by-step explanation:
Let's write an equation for the area of this figure.
This figure can be divided into 2 rectangles, a vertical and horizontal rectangle.
Area of rectangle= length× breadth
Area of vertical rectangle= 6x
Length of horizontal rectangle= (7 -x) cm
Area of horizontal rectangle= x(7-x)
Since total area= 30 cm^2,
6x+ x(7-x)= 30
6x +7x -x^2= 30 (expand)
-x^2 +13x-30= 0 (bring all terms to one side)
x^2 -13x +30= 0 (divide by -1)
(x -10)(x -3)= 0 (factorise)
x -10= 0 or x -3= 0
x= 10 or x= 3
(reject)
We reject x=10 since from the diagram, x cm is less than 6cm.