Question

Is this correct? question:
Two triangular roofs are similar. The ratio of the corresponding sides of these roofs is 2:3. If the altitude of the smaller roof is 4.5 feet, find the corresponding altitude of the larger roof. Round to the nearest hundredth.

my answer:
ratio = 2:3
altitude of the larger roof:

4.5/2 * 3 =

6.75 feet

Answer 1

@Loser66 @pooja195 @zepdrix

Answer 2

@Loser66 @pooja195 @zepdrix

Answer 3

let Bb and Bs be the sides of the big and small triangles respectively. and also
let Ab and As be the corresponding altitudes.
Bs/Bb= As/Ab = 2/3 :ratio is (2:3)
2/3 = As/Ab or As = (2/3)(Ab) = (2/3)*(4.5) = 3 ft
Altitude of the smaller roof is : 3 ft <= ans


I believe this is right but not 100% sure...

Answer 4

@zepdrix

Answer 5

@Awolflover1

Answer 6

yup

Answer 7

In your shoes I would sketch these two triangular roof sections and label everything. What measurements (dimensions) would you need to have / know to find the altitude of one such triangle?

Can you use the given 2:3 ratio to determine the alt. of the larger roof, or must you use some other formula to find this altitude? Perhaps you could try doing this both ways and then be better prepared to answer this question.

Answer 8

You solved the problem correctly.

Answer 9

actual dimensions: smaller altitude 4.5 larger altitude x
ratio: smaller triangle 2 larger triangle 3

proportion: \(\dfrac{4.5}{2} = \dfrac{x}{3} \)

\(x = \dfrac{3 \times 4.5}{2} = 6.75\)

which is exactly what you got.

Good job as usual!

Answer 10

Thanks!

Answer 11

yw