Question

The shape in the quilt block is shown is an isosceles triangle, where AB equals AC. The perimeter of the triangle is 27.3 inches. Find the values of X and Y. Then, find the length of each side of a triangle

Answer 1

(X, Y) = (3, 5)

AB = AC = 8

BC = 11.3

Explanation:

The difference between sides AB and AC is zero:

AC -AB = 0

(6X -2Y) -(X +5) = 0

5X -2Y -5 = 0

The difference between the sum of sides and 27.3 is zero:

AC +AB +BC -27.3 = 0

(6X -2Y) +(X +5) +(Y +6.3) -27.3 = 0

7X -Y -16 = 0

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To solve these, we can subtract the first equation from twice the second to eliminate Y.

2(7X -Y -16) -(5X -2Y -5) = 2(0) -(0)

9X -27 = 0 . . . . simplify

X -3 = 0 . . . . . . . divide by 9

X = 3

Substituting into the second equation gives ...

7(3) -Y -16 = 0

5 = Y . . . . . . . . . . add Y

The solution for X and Y is X = 3, Y = 5.

AB = AC = X+5 = 8

BC = Y +6.3 = 11.3

The side lengths are AB = AC = 8, and BC = 11.3.