Question

The base of triangle $T$ is $40$ percent less than the length of rectangle $R$. The height of triangle $T$ is $50$ percent greater than the width of rectangle $R$. The ratio of the area of triangle $T$ to that of the area of rectangle $R$ converted to $\%$ is :

• A. $10$
• B. $45$
• C. $90$
• D. $110$

Answer 1

The correct option is B $45$

Area of triangle $=\frac{1}{2}\times$ base $\times$ height

Area of rectangle = length $\times$ breadth

Let length of rectangle $R$ be $L$. So, the base of triangle $T$ becomes $0.6L$

Let the width of the rectangle $R$ be $W$. The height of the triangle thus becomes $1.5W$

Area of rectangle $=LW$

Area of triangle $=\frac{0.6L\times 1.5W}{2}=0.45LW$

Ratio of the areas when converted to percentage thus becomes $\frac{0.45LW}{LW}\times 100=45$