Question

Area of a square is 4 sq. m more than 2/3 of area of a rectangle. If the area of square is 64 sq.m, then find the dimensions of rectangle, given that breadth is 2/5 of length.

plz solve this......​

Answer 1

$\bf \underline{Given}$

• Area of square = 64m²
• Area of square = 4m² + 2/3 of area of rectangle
• Breadth of rectangle = 2/5 of length

$\bf \underline{ To \: Find}$

• Length and breadth of rectangle.

$\bf \underline{ Using \: Formula }$

$\sf\bullet \: \underline{\red{ Area \: of \: rectangle \: = \: length \times breadth }}$

$\sf\bullet \: \underline{\red{ Area \: of \: square = side \: \times \: side }}$

Let the length of rectangle be x.

Breadth of rectangle = 2/5 of length = 2x/5

Since, area of square is 4 more than 2/3 of area of rectangle.

∵ Area of square- (4) = 2/3 × x × 2x/5

$\sf \implies 64m {}^{2} - 4 = \dfrac{2x}{3} \times x \times \dfrac{2}{3}...(ar. \: of \: square = 64m {}^{2} ) \: \\ \sf \implies \: 60m {}^{2} = \frac{4x {}^{2} }{15} \\ \sf \implies \: x {}^{2} = 60 \times \frac{15}{4} \\ \sf \implies x{}^{2} = 225 \\ \sf \implies \: x {}^{2} = \sqrt{225} \\ \sf \implies \: x = 15m$

$\large \implies \boxed {\boxed {\tt \blue {Length = x = 15m}}}$

$\large \implies \boxed {\boxed {\tt \blue {Breadth =\frac{2x}{5} = 6m}}}$