Question

Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms? A. (3 × 13^2) + (2 × 15^2) B. (2 × 13^3) + (2 × 15^2) C. (3 × 15^2) + (2 × 13^2) D. (3 × 13^2) × (2 × 15^2)

Answer 1

A.
`(3*13^2)+(2*15^2)`

Explanation:

The area of a square can be calculated with this formula:

`A=s^2`

Where "s" is the lenght of any side of the square.

You know that any side of three square rooms measure 13 feet each and any side of two square rooms measure 15 feet each.

Let be
`s_1` the lenght of any side that measures 13 feet and and
`s_2` the lenght of any side that measures 15 feet.

Then, the total area will be:

`A_(total)=3(s_1)^2+2(s_2)^2\\\\A_(total)=(3*13^2)+(2*15^2)`

Therefore, the expression that shows the total area of these five rooms is the expression shown in the option A.

Answer 2

The total area of the five rooms = 3 × 13² + 2 × 15² ⇒ answer A

Explanation:

* lets revise the area of the square

- The area of any square is (the length of its side)²

- We have five room

- Three of them have side length 13 feet each

- Two of them have side length 15 feet each

* lets find the total area of the five room

- The area of the three rooms of side length 13 feet

∵ The length of the side of each square is 13 feet

∴ The area of each room of the three = 13²

∴ The total area of the three rooms = 3 × 13² feet² ⇒ (1)

- The area of the two rooms of side length 15 feet

∵ The length of the side of each square is 15 feet

∴ The area of each room of the two = 15²

∴ The total area of the three rooms = 2 × 15² feet² ⇒ (2)

- To find the area of the five rooms and (1) and (2)

∴ The total area of the five rooms = 3 × 13² + 2 × 15²