FIRSTLY: John has a slice of pizza in the exact shape of an isosceles triangle. 2 sides measure Y + 5 and 1 side measures Y – 2. Write an expression for the total perimeter. SECONDLY: Multiply out the following brackets: (3Y + 8)(3Y + 2)
First part: An isosceles triangle has 2 sides of the same length and 1 side of a different length. 2 of these sides: 2 x (Y + 5) = 2Y + 10. 1 side: Y – 2. The perimeter is the total ‘edge’ of the shape. (If you traced the edge of the pizza with your finger, along all 3 sides of the triangle slice, that would be the perimeter). THEREFORE: We add the 3 sides altogether -> Perimeter: 2Y + 10 + (Y – 2) = 3Y + 8. Second part: The simplest way is to use the FOIL technique, when multiplying out brackets. (First, Outside, Inside, Last). Firstly, we multiply out the ‘first’ part. This is 3Y x 3Y = 9Y2 (3Y + 8)(3Y + 2) = 9Y2 ... Next, we do the outside bit, which is 3Y x 2 = 6Y. Then, the inside bit is 8 x 3Y = 24Y. (3Y + 8)(3Y + 2) = 9Y2 + 6Y + 24Y ... Finally, we do the ‘last’ bit. This is 8 x 2 = 16. Adding this altogether, we get a final answer of: (3Y + 8)(3Y + 2) = 9Y2 + 30Y + 16
