Yr 9 Algebra Investigation

Mr. Gershwin is trying to find the right size grand piano to fit into his Room. The size of the room in his apartment is represented by a rectangle whose sides are described by the expressions 4x – 4 and 8x – 8.

Introduction
I believe the aim of the investigation was to find a perfect sized piano for Mr. Gershwin’s apartment.

Mathematical Investigations

1. Mr Gershwin wants to buy a rectangular piano which is half the width and length of the room. Find the expressions for the length of each side of the piano. Answer; In the mathematical expression for the room was in (4x – 4) (8x – 8) metres. The question asks us to half the length and width of the room by finding the expression of the length of each side of piano therefor the answer is half of the above expression so therefore it would be (2x-2) (4x-4).

2. Find the perimeter of the piano and also the room in expressions. Have these expressions Simplified if possible. Answer;

(4x-4)

(8x-8)

Room: 24x-24
Piano: 12x-12

3. For a value of x = 3, find the area of the piano and the area of Mr Gershwin’s room. What area of the room is not occupied by the piano? Room (24(3)-24) =48 sq meters Piano (12(3)-12) =24 sq meters Unoccupied by the piano; 24sq.m

4. Mr Gerswin decides the piano will be much too large. If the size of the piano is halved again and let , what area of the room will not be occupied by the piano?
Room; (24(2)-24) = 24sq meters
Piano; (12(2)-12) = 12sq meters

Unoccupied by the piano: 36 sq. m

(4x-4)

(8x-8)