Question

A rectangle and a rhombus are on the same base and between the same parallels. Then the ratio of their areas is

• A. $1:1$
• B. $1:2$
• C. $1:3$
• D. $1:4$

Answer 1

The correct option is A $1:1$

Let ABCD be a rectangle and EFCD be rhombus with the same base CD & between same parallel lines.

Now, in $△$ & $ABD$ & $BFC$;

$\angle EAD=\angle FBC\left[Each{90}^0\right]$

$AD=BC$ [Opposite sides of rectangle ABCD]

$ED=FC$ [Sides of the rhombus]

$\therefore$ $△EAD\cong △FBC$ [ By right angle hypotenuse side congruency]

$\therefore ar△EAD=ar△FBC$

Adding both sides, $\left(ar\square EBCD\right)$, we get

$ar△EAD+arEBCD=ar△FBC+arEBCD$

$arABCD=arEFCD$

Thus the rectangle & the rhombus with same base & between same parallels have equal areas.

Thus the ratio of area is $1:1$.