Question

While reading a newspaper, Ted caught news of a football match between Brazil and Spain. The countries were represented with their respective flags. In Brazil’s flag, the length of any side of the parallelogram is 10.6 cm and the corresponding height is equal to 8.3 cm. If the area of the green region is 74.02 $c{m}^2$ and length of the flag is twice the breadth, find the length of the flag.

• A. 9 cm
• B. 18 cm
• C. 9.5 cm
• D. 19 cm

Answer 1

The correct option is B

18 cm

Given the base of the parallelogram is 10.6 cm and the corresponding height is 8.3 cm.

Area of the parallelogram = base × height = (10.6 $\times$ 8.3) $c{m}^2$ = 87.98 $c{m}^2$.

The total area of the flag = area of parallelogram + area of the green part

= 87.98 $c{m}^2$ + 74.02 $c{m}^2$

= 162 $c{m}^2$.

Let the breadth of the flag be $x$.

Then, the length of the flag = 2$x$.

Area of the flag = 2$x$ $\times$$x$ = $2x^2$.

So, $2x^2$ = 162

or, $x^2$ = 81

or, $x$ = 9.

So, the length of the flag = 2$x$ = 2 $\times$ 9 cm = 18 cm.