The ratio Of perimeters of two isosceles right triangles is 1 to 3 if the length of the hypotenuse of the larger triangle is 18 find the length of the hypotenuse of the smaller triangle

The length of the hypotenuse of the smaller triangle is 6

Step-by-step explanation: The first clue provided in the question states that both isosceles triangles are similar. That means there is a ratio that is common to all sides of both triangles. The ratio of similarity of both perimeters is given as 1:3. That is for every measurement taken in the smaller triangle, the larger triangle would be equal to times 3. Similarly, for every measurement taken in the larger triangle, the smaller one would be equal to divided by 3.

The hypotenuse of the larger one is given as 18 units, therefore the hypotenuse of the smaller one would be

18 divided by 3 which equals 6.

Therefore the length of the hypotenuse of the smaller triangle is 6.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.