The width of a rectangle is the length minus 6 units. The area of the rectangle is 27 units. What is the length, in units, of the rectangle?

9 units

Step-by-step explanation:

Area of rectangle= length ×width

Let the length of the rectangle be x units.

Width of rectangle= (x -6) units

Area of rectangle= 27 units²

x(x -6)= 27

x(x) -x(6)= 27          (expand bracket)

x² -6x -27= 0

(x -9)(x +3)= 0        (factorise)

x -9= 0  or  x +3= 0

x= 9       or       x= -3 (reject)

∴ The length of the rectangle is 9 units.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.