Question 9 - (3 marks available)

Tri

Use similar triangles to calculate the height, h cm, of triangle ABE.

10 cm

36 cm

20 cm

Image of the triangle is attached

24 cm

Step-by-step explanation:

If two triangles are similar, the corresponding sides must be in the same ratio.

From the diagram, the height of the triangle is 36cm.

But the height of triangle ABE = h,

To find the height of triangle BCD, let's subtract the height of triangle ABE from 36cm.

Therefore.

Height of BCD = 36 - h.

Since the triangles are similar and their corresponding sides have the same ratio, we have the expression:

Substituting figures, we have:

Cross multiplying, we have:

20(36-h) = 10 * h

720 - 20h = 10h

720 = 10h + 20h

720 = 30h

h = 24 cm

Therefore, the height of triangle ABE is 24cm

if x = 1, then the answer is 3.5

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.