Can anyone tell me how to answer these geometry questions?
2) Suppose a regular quadrilateral and a regular triangle have the same perimeter. The sides of the triangle are 3 inches longer than the sides of the quadrilateral. Find the lengths of the sides of the quadrilateral and the triangle.
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2 – 3y = 2y + 3
so 28 – 3 = 2y + 3y
so 5y = 25
so y = 5
28 – 3(5) = 28 – 15 = 13
and 2(5) + 3 = 10 + 3 = 13
So, the perimeter of the triangle is 13(3) = 39
2 – Again, I’m assuming regular to be equilateral. If the perimeters are equal, and we assign a value of x as a variable for one side of the triangle and y as a variable for one side of the quadrilateral, we can say that the perimeter of the triangle is 3x (three sides times some value x) and the perimeter of the quadrilateral is 4y (four times some value y). So 3x = 4y.
Just off the top of my head, I can see that the value of x is 4 and the value of y is 3 (3 x 4 = 12). That then becomes the ratio of lengths of the sides of each object to the other object.
If the difference in length of one side of the triangle compared to the quadrilateral is 3 inches and the ratio is 4 to 3, we then have to multiply each of the parts of the ratio by 3 to get a difference of 3 inches.
So, the length of the sides of the triangle is 4(3) = 12
and the length of the sides of the quadrilateral is 3(3) = 9.
And, the difference between 12 and 9 is 3. So, those numbers are correct.
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