Question

Three squares have perimeter of $12$ m, $20$ m and $24$ m respectively. If a rectangle is constructed whose area is equal to the combined area of the three squares such that its width is $7$ m, then the length of the rectangle is

• A. $6$ m
• B. $8$ m
• C. $10$ m
• D. $12$ m

Answer 1

The correct option is C $10$ m

Side of square $1=\frac{12}{4}=3m$

Side of square $2=\frac{20}{4}=5m$

Side of square $3=\frac{24}{4}=6m$

Let length of rectangle be 'l' then,

$l\times 7={\left(3\right)}^2+{\left(5\right)}^2+{\left(6\right)}^2\Rightarrow l=\frac{70}{7}=10$m

$\therefore$ Length of rectangle$=10m$