Question

The ratio of the areas of two similar right triangles is 9 : 16. The length of one of the sides of the smaller triangle is 15 cm. How much longer is the length of the corresponding side of the larger triangle from smaller triangle? ​

Answer 1

Answer:

5. (longer side is 20)

Step-by-step explanation:

let us assume that the two triangles are ABC and DEF, with AB = 15. we need to find DE.

we know that the area(ABC)/area(DEF) = 9/16 = (AB)^2/(DE)^2

= (AB/DE)^2 = (3/4)^2

= AB/DE = 3/4

now that we know the ratio between the sides, we can substitute the values-

15/DE = 3/4

= 15 * 4 = 3 * DE

= 60/3 = DE = 20

since we need to know how much longer it is from AB, we just need to subtract AB from DE

DE - AB = 20 - 15 = 5

therefore, the answer is 5.