Question

= 2 8 cm 6 cm 9 cm 12 cm base height original height reduction base reduction 8 = 6 72 = 72

Answer 1

The large triangle is 1.5 times of the small triangle.

The small triangle is (1/1.5) or (2/3) of the large triangle.

Step-by-step explanation

The solution of this question applies the rule of similar triangles.

The larger triangle has height 8 cm and base length 12 cm.

The smaller triangle has height 6 cm and base length 9 cm.

The similar triangle principle is then given as

`\begin{gathered} \frac{Height\text{ of the large triangle}}{Height\text{ of the small triangle}}=\frac{Base\text{ length of the large triangle}}{Base\text{ length of the small triangle}} \\ \text{Substituting the values for these} \\ (8)/(6)=(12)/(9) \\ \text{Cross multiply} \\ 8*9=12*6 \\ 72=72 \end{gathered}`

So, the reduction can be given through the ratio of the heights or the base lengths of the triangles.

`(8)/(6)=(12)/(9)=(3)/(2)=1.5`

Hence, the large triangle is 1.5 times of the small triangle.

The small triangle is (1/1.5) or (2/3) of the large triangle.

Hope this Helps!!!