Question

In the figure, $LMNO$ and $GHJK$ are rectangles where $GH=\frac{1}{2}LM$ and $HJ=\frac{1}{2}MN$. What fraction of the region is bounded by $LMNO$ that is not shaded?

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{3}{4}$

Answer 1

The correct option is D $\frac{3}{4}$

Area of rectangle $LMNO=MN\times LM$
And, Area of rectangle $GHJK=GH\times HJ=\frac{1}{2}LM\times \frac{1}{2}MN=\frac{1}{4}\times (LM\times MN)=\frac{1}{4}$(Area of rectangle $LMNO$)
Hence, part of the region is bounded by $LMNO$ that is not shaded $=$ Area of rectangle $LMNO-$ Area of rectangle $GHJK=$ Area of rectangle $LMNO-\frac{1}{4}$ (Area of rectangle $LMNO)=\frac{3}{4}$ (Area of rectangle $LMNO$)
Hence, fraction of the region that is not shaded $=\frac{\left(\frac{3}{4}\right)\left(\text{Area of rectangle LMNO}\right)}{\text{Area of rectangle LMNO}}=\frac{3}{4}$