Question

Use an algebraic equation to solve the problem. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 90 cm?

A. 10.5 cm, 11.5 cm, and 12.5 cm

B. 22.5 cm, 30 cm, and 37.5 cm

C. 7.5 cm, 11.5 cm, and 32.1 cm

D. 19.3 cm, 25.7 cm, and 32.1 cm

Answer 1

Ratio units = 3+4+5 = 12

perimeter = 90 (a+b+c)

1 unit value, 90/12 = 7.5

So, lengths will be 3(7.5), 4(7.5), 5(7.5)

OPTION B IS YOUR ANSWER

Answer 2

The answer is the option B

`22.5\ cm, 30\ cm, 37.5\ cm`

Explanation:

Let

a,b,and c the length sides of the triangle

we know that

`a+b+c=90` ------> equation A

`(a)/(b)= (3)/(4)`

`a=(3)/(4)b` -----> equation B

`(b)/(c)= (4)/(5)`

`c=(5)/(4)b` -----> equation C

Substitute the equation B and equation C in the equation A

`(3)/(4)b+b+(5)/(4)b=90`

solve for b

`3b=90`

`b=30\ cm`

Substitute the value of b in the equation B

`a=(3)/(4)(30)=22.5\ cm`

Substitute the value of b in the equation C

`c=(5)/(4)(30)=37.5\ cm`