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

A?

Answer 2

@I4NI

Answer 3

@Chlorophyll

Answer 4

i think im way off hahah

Answer 5

B = 90

Answer 6

Hmm..
\[a ^{2}+b ^{2}=c ^{2}\] I wanted to check if it was going to be a right triangle, so using the ratios I plugged them in to find out;
\[3:4:5\]\[3^{2}+4^{2}=5^{2}\]\[9+16=25\]\[25=25\]So, it is a right triangle, meaning one of the answers has to fit with the equation of the Pythagorean Theorem;\[a ^{2}+b ^{2}=c ^{2}\] So let's try them out until we hit one that works;

A) 10.5cm, 11.5cm, 12.5cm
\[10.5^{2}+11.5^{2}=12.5^{2}\]\[110.25+132.25=156.25\]\[242.5=156.25\]It is false, so the answer is not A.

B) 22.5cm, 30cm, 37.5cm
\[22.5^{2}+30^{2}=37.5^{2}\]\[506.25+900=1406.25\]\[1406.25=1406.25\]
Ding ding ding...we have a winner! The answer is B. I could figure out the rest if you wish, or maybe you can instead.

Answer 7

i already finished it and got an answer plus i found an easy way to do it lol