Question

A triangle with an area of 10 square meters has a height of 4.5 meters. A similar triangle has an area of 90 square meters. What is the height of the larger triangle?

A) The ratio of the area of the small triangle to the area of the larger triangle is _:_
B) The ratio of the side length of the small triangle to the side length of the larger triangle is _:_

Answer 1

h = 40.5 m

A) 1 : 9

B) 1 : 3

Explanation:

Let the height of the larger triangle be h

Therefore,

`(10)/(90)= (4.5)/(h)\\\\</p><p>(1)/(9)= (4.5)/(h)\\\\</p><p>h = 9* 4.5\\\\</p><p>h = 40.5\:m\\`

A)

The ratio of the area of small triangle to the large triangle

`=(10)/(90)=(1)/(9)=1 : 9`

B)

The ratio of the side length of small triangle to the side length of large triangle

`=\sqrt{(10)/(90)} =\sqrt {(1)/(9)} =1 : 3</p><p>`