Question

Area of a square is \[4{m^2}\] more than \[\dfrac{2}{3}\] of an area of the rectangle. If the area of the square is \[64{m^2}\] . Find the dimension of the rectangle given that breadth is \[\dfrac{2}{5}\] of the length.

Answer 1

Hint: Area is measured in "square" units. Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared.
If a square has one side of 4 inches, the area would be 4 inches times 4 inches, or 16 square inches.

Complete step by step answer:
Given that the Area of a square is 4sq.m more than\[\dfrac{2}{3}\] the area of a rectangle. If the area of the square is 64sq.m. then find the dimensions of the rectangle, given that breadth is of \[\dfrac{2}{5}\] length.
Let the length of the rectangle be L
Let the breadth of the rectangle be B
Given B=\[\dfrac{2}{5}\]L……(i)
Area of the square = 64 sq.m.
Area of the square is 4 sq.m. more than \[\dfrac{2}{3}\] of the rectangle
Area of rectangle is \[\dfrac{3}{2} \times \left( {64 - 4} \right) = 90\]
Therefore,
 \[ \Rightarrow \] L\[ \times \]B\[ = 90\]
 \[ \Rightarrow \] \[L \times \dfrac{2}{5}L = 90\]
 \[ \Rightarrow \]\[L = 15\]
Hence putting the value of L=15m in equation (i) we get
B=\[\dfrac{2}{5}L\]
\[ \Rightarrow B = \dfrac{2}{5} \times 15 = 6m\]
Hence the dimensions of the rectangle are:
Length=15m
Breadth=6m

Note: Be sure to use the same units for all measurements. You cannot multiply feet times inches, it doesn't make a square measurement.
The area of a rectangle is the length on the side times the width. If the width is 4 inches and the length is 6 feet, what is the area?
NOT CORRECT .... 4 times 6 = 24
CORRECT.... 4 inches is the same as 1/3 feet. Area is 1/3 feet times 6 feet = 2 square feet. (or 2 sq. ft., or \[2f{t^2}\] ).