A rectangle and a square are joined together to make a larger rectangle with a perimeter of 40cm . If the square has an area of 49cm^(2) , what is the area of the original rectangle? Give your answer in cm^(2) .

Question

A rectangle and a square are joined together to make a larger rectangle with a perimeter of 40cm . If the square has an area of 49cm^(2) , what is the area of the original rectangle? Give your answer in cm^(2) .

Answer 1

First, note that the square has an area of 49 cm^2 which means a side length of 7 cm (since 7*7 = 49). Then, remember that a square joined with the original rectangle forms a new rectangle with a perimeter of 40 cm. Since the perimeter of a rectangle = 2*length + 2* width, and we know the length is equal to 7 cm (as it's shared with the square), call "x" for the width of the bigger rectangle. Hence, 2*7 + 2*x = 40, simplifying that gives x = 13 cm. Thus, the width of the original smaller rectangle is 13 – 7 = 6 cm. Finally, the area of the rectangle= length *width= 7*6 = 42 cm^2.

Question

A rectangle and a square are joined together to make a larger rectangle with a perimeter of 40cm . If the square has an area of 49cm^(2) , what is the area of the original rectangle? Give your answer in cm^(2) .

Answer

Answer

Explanation