How would I solve these two word problems that are in Geometry?

Question

I need help how to solve these kind of geometry word question which have something like, an triangle as 3 time less then the length of the othere side. here is two question, i want to use these two different question to work on the other question that I have.

1-If two side of the triangle are equal in length and the third side is 6 inches less than the length of the one of the equal sides, find the length of the side if the perimter is 24 inches. Geometric principle: the perimtere of a triangle is equal to the sum of the lengths of it's side.

 

2-The permeter of a rectangle is 42 inches and the length is 3 times the width. find it's demensions geoetric principle: the Permeter of the rectangle is  P=21+2w

also for numer two, if it say something different like "the length is 3 inches less then the width" what would I do next?

 

P.s Thanks you in Advance for helping me with two of these long question.!

-John

Answer 1

1)

Side 1: x

Side 2: x

Side 3: x-6

Perimeter: 24

x + x + x - 6 = 24

3x - 6 = 24

3x = 30

x = 10

Side lengths: 10, 10, 4

.

Perimeter = 2L + 2W

L = 3W

Perimeter = 3W + 2W

Perimeter = 5W

Perimeter = 42

5W = 42

W = 42/5 = 8.4

L = 3W

L = 3(42/5)

L = 126/5 = 25.2

Answer:  Length = 25.2 inches, width = 8.4 inches

Note:  P does not equal 21 + 2W

If you say something like "the length is 3 inches less than the width," that means you call the width x and the length x - 3.