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The base of an isosceles triangle is three times as long as the side of a square. Each leg of the triangle is 1 inch more than twice a side of the square. Find the length of a leg of the triangle if the sum of perimeters is 46 inches.

Sagot :

Answer:

9 inches

Step-by-step explanation:

Let x be the length of the side of the square.

If the base of the triangle is 3 times as long as the side of the square, it is 3 times x, or 3x.

The same can be said for the legs, which is 1 inch more than twice the side of the square, so 2x + 1.

The triangle can therefore be thought to look like the triangle below.

The perimeter is therefore (2x+1) + (2x+1) + 3x, which is 7x + 2.

The sum of perimeters of both the square and triangle is 46.

The perimeter of the square is 4x, so the sum of perimeters is 4x + (7x+2), or  11x + 2.

11x + 2 = 46, so 11x = 44.

x is therefore 4

The leg is 2x + 1, so the leg is 8 + 1, so the length of the leg is 9 inches.

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