Question

A mirror is made of two congruent parallelograms as shown in the diagram. The parallelograms have a combined area of $7\frac{1}{2}$ square units. If the height of each parallelogram is $1\frac{1}{3}$ units, then find the base of each of them.

• A. $4\frac{1}{2}$ units
• B. $2\frac{13}{10}$ units
• C. $3\frac{13}{16}$ units
• D. $2\frac{13}{16}$ units

Answer 1

The correct option is D $2\frac{13}{16}$ units


Given: Area of two parallelograms $=7\frac{1}{2}$, Height $=1\frac{1}{3}$

Area of one parallelogram $=\frac{7\frac{1}{2}}{2}$

$7\frac{1}{2}=\frac{7\times 2+1}{2}=\frac{15}{2}$

Area of one parallelogram $=\frac{15}{2}\times \frac{1}{2}=\frac{15}{4}$ square units

Base $\times$ Height $=\frac{15}{4}$

Base $\times 1\frac{1}{3}=\frac{15}{4}$

$1\frac{1}{3}=\frac{1\times 3+1}{3}=\frac{4}{3}$

Base $\times \frac{4}{3}=\frac{15}{4}$

Base $=\frac{45}{16}$ units

Base $=\frac{45}{16}=2\frac{13}{16}$ units