Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
$A B C D$ is a rectangle and $A B E$ is a triangle whose vertex $E$ lies on $C D$. If $A B=5 \mathrm{cm}$ and the area of the triangle is 10 sq. cm, then the perimeter of the rectangle is
(a)14 cm
(b)15 cm
(c)18 cm
(d)20 cm
Answer
Answer (as printed): C
Explanation
Area of $\triangle A B E=\frac{1}{2} \times A B \times E F=\frac{1}{2} \times A B \times B C$. $\therefore \quad \frac{1}{2} \times A B \times B C=10 \Rightarrow \frac{1}{2} \times 5 \times B C=10 \Rightarrow B C=\frac{2 \times 10}{5}=4$. Perimeter of rectangle $A B C D=2(A B+B C)=[2(5+4)]$ $\mathrm{cm}=18 \mathrm{cm}$.