Quote:
PQRS is a rectangle and OPQ is a triangle with side PQ=6 units. With O as the centre point of RS.
What is the area of the rectangle PQRS?
1) Perimeter of isosceles triangle OPQ is 16 units.
2) Area of triangle OPQ is 12 square units.
Statement 1Since it is given the triangle is isosceles with base PQ, we can say that:
OP + PQ + OQ = 16
As O is the centre of RS, OP=OQ
Therefore, OP=OQ=5
With Pythagoras, we can find the value of RQ which comes to 4.
As we know the length and the width of the rectangle, we can calculate the area.
Hence, Statement 1 alone is sufficient.
Statement 2Area of triangle OPQ is given as 12 sq units.
Area of triangle = 1/2 * base * height
Therefore, 1/2 * 6 * height =12 ................(Base is PQ = 6 units)
height= 4 units
The height of the triangle is also the width of the rectangle
As we know the length and the width of the rectangle, we can calculate the area.
Hence, Statement 2 alone is sufficient.
Both Statements are sufficient to answer the question.
Answer is D