Question

Ratio of areas of two similar triangles is 49: 64 and perimeter of smaller triangle is
21cm then the perimeter of the bigger triangle is
A) 32 cm
B) 15 cm
C)
24 cm
D) 16 cm​

Answer 1

Answer:

hey here is your solution

pls mark it as brainliest

Step-by-step explanation:

so let the two similar triangles be triangle ABC and triangle XYZ such that triangle ABC is smaller triangle and the other is bigger

so as triangle ABC is similar to triangle XYZ

by theorem on ratios of areas of similar triangles

we get

A(Triangle ABC)/A(Triangle XYZ)=AB²/XY²

so here

A(Triangle ABC)/A(Triangle XYZ)=49/64

thus then

49/64=AB²/XY²

taking square roots on both sides we get

AB/XY=7/8

so as triangle ABC is similar to triangle XYZ

AB/XY=BC/YZ=AC/XZ=7/8 (c.s.s.t)

thus

now AB=7XY/8

BC=7YZ/8

AC=7XZ/8 (1)

so here perimter of triangle ABC=21 cm

thus then

AB+BC+AC=21

7XY/8+7YZ/8+7XZ/8=21

7XY+7YZ+7XZ/8=21

7(XZ+YZ+XZ)/8=21

ie XY+YZ+XZ=3×8

so XY+YZ+XZ=24 cm

hence perimter of triangle XYZ=24.cm

so perimter of bigger triangle is 24.cm