Question

Check up 1

Answer 1

Answer:

a. The expression for the area of the gym is 15·x

b. The expression for the area of the cafeteria is 15·x + 45

c. The expression for the total area of the gym and the cafeteria is 30·x + 45

d. The expression for the total perimeter of the gym and the cafeteria is 36 + 4·x

Step-by-step explanation:

The parameters of the given figures are;

The width of the figure, w = 15

The breadth of the gym, $b_{gym}$ = x

The breadth of the cafeteria, $b_{cafeteria}$ = x + 3

The shape of the area of the gym = A rectangle

The shape of the area of the cafeteria = A rectangle

a. The expression for the area, 'A₁', of the gym is given by the area of a rectangle which is Width × Breadth

The area of the gym, A₁ = The width of the figure × The breadth of the gym

Therefore, we have; The area of the gym, A₁ = w × $b_{gym}$

A₁ = 15 × x

The area of the gym, A₁ = 15·x

b. The area of the cafeteria, A₂ = The width of the figure × The breadth of the cafeteria

The area of the cafeteria, A₂ = w × $b_{cafeteria}$

∴ A₂ = 15 × (x + 3) = 15·x + 45

The expression for the area of the cafeteria, A₂ = 15·x + 45

c. The expression for the total area of the gym and the cafeteria, 'A', is given as follows;

A = A₁ + A₂

∴ A = 15·x + 15·x + 45 = 30·x + 45

The expression for the total area of the gym and the cafeteria = 30·x + 45

d. The expression for the total perimeter of the gym and the cafeteria, 'P', is given as follows;

P = The perimeter of the rectangular area of the gym plus the area of the cafeteria

∴ P = 2 × 15 + 2 × (x + x + 3)

P = 30 + 4·x + 6

P = 36 + 4·x

The expression for the total perimeter of the gym and the cafeteria P = 36 + 4·x.