Question

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

Answer 1

⋆ $\bold{\underline{\underline{\rm{\red{Correct \; Question:-}}}}}$

• Area of a square is 4 sq. M more than $\sf{ \dfrac{2}{3}}$ of the area of a rectangle. If the area of square is 64 sq. M, then find the dimensions of rectangle, given that breadth is $\sf{ \dfrac{2}{5}}$ of length.

⋆ $\bold{\underline{\underline{\rm{\blue{Given:-}}}}}$

• Area of a square is 4 m² more than $\sf{ \dfrac{2}{3}}$ of the area of a rectangle.

• If the area of square is 64 m² then breadth is $\sf{ \dfrac{2}{5}}$ of length.

⋆ $\bold{\underline{\underline{\rm{\purple{To\;Find:-}}}}}$

• Dimensions of Rectangle.

⋆ $\bold{\underline{\underline{\rm{\pink{Solution:-}}}}}$

★ Let length of rectangle = l

★ Let breadth of rectangle = b

$\bold{\underline{\underline{\sf{\red{\dag \; According\;to\;question:-}}}}}$

$\implies \sf{b = \dfrac{2}{5} l}$ ...[eq.(1)]

✦ Area of square = 64m²

✦ Area of a square is 4 m² more than $\sf{ \dfrac{2}{3}}$ of the area of a rectangle.

$\implies \sf{Area\;of\: Rectangle\; is\; \dfrac{3}{2} \times (64 - 4) = 90}$

$\implies \sf{Area\;of\: Rectangle= l \times b = 90}$

$\implies \sf{l \times \dfrac{2}{3} l = 90}$

$\implies \sf{2l^2 = 450}$

$\implies \sf{ \sqrt{l^2} = \sqrt{225}}$

$\implies {\underline{\underline{\boxed{\sf{\purple{l = 15}}}}}}$

∴ Put the value of l in equation (1):-

$\implies \sf{b = \dfrac{2}{ \cancel{5}} \times \cancel{15}}$

$\implies {\underline{\underline{\boxed{\sf{\purple{b = 6}}}}}}$

Hence,

✧ The length of rectangle is 15m.

✧ The breadth of rectangle is 6m.

$\rule{200}3$