To solve questions like this, I always recommend drawing a picture. A picture helps you visualize the problem.
Then you need to know the equation for the perimeter. The perimeter, P, of a shape is the distance around. For a rectangle, P = l + w + l + w, where l = length, w = width. The order doesn't matter so you can rewrite this as P = 2l + 2w.
Next, you need to translate the sentences into equations. When I taught algebra, I had students write a "math/English" dictionary that shows the translation of words in English to mathematical symbols.
Sentence 1: The perimeter of the rectangle is 194. ==> P = 194
Sentence 2: The length is 25 more than 5 times the width. ==> l = 25 + 5w
From prior understanding, we know that P = 2l + 2w.
Combining this with Sentence 1, we get P = 2l + 2w = 194
Using sentence 2, we can replace l with its equivalent expression in terms of w, so that we get a single equation with one unknown: 2(25 + 5w) + 2w = 194
Apply PEMDAS and reduce the equation: 50 + 10w + 2w = 50 + 12w = 194
Solve for w: 50 - 50 +12w = 194 - 50= 144 ==> 12w/12 = 144/12 ==> w = 12
Substitute the value of w back into the sentence 2 equation to solve for l
l = 25 + 5w = 25 + 5*12 = 85
Check the solution using the equation for perimeter: P = 2l + 2w = 194
2(85) + 2(12) = 170 + 24 = 194. Solution is verified.
These are steps worked out that you can apply to any type of problem. Visualize the problem, identify any prior knowledge equations needed to solve the problem. Identify any unknown and/or known variables/values Use the information given to construct the relationships between the variables, Substitute reduce the problems to single unknown with single equation, solve.