Question

the area of a rectangle is 582sq.m. the length is one more than twice of the breadth.find the length and breadth.​

Answer 1

Given:

Area of the rectangle = 528 m²

Now:

Let the breadth of the rectangle be 'x' m.

Length of the rectangle = (2x + 1) m

We know that:

$\boxed{\sf{ \pink{Area\:of\:the\:rectangle = l \times b}}}$

$\implies \sf (2x + 1) × x = 528$

$\implies \sf \: 2x² + x - 528 = 0$

$\implies \sf 2x² + 33x - 32x - 528 = 0$

• By middle term splitting:

$\implies \sf x(2x + 33) - 16(2x + 33) = 0$

$\implies \sf(x - 16) (2x + 33) = 0$

$\implies \sf \: (x - 16) or (2x + 33) = 0$

We get:

$\large{ \leadsto}\boxed{\sf{ \pink{x = 16\:or\:x =-\frac{33}{2}}} }$

Since:

The breadth can't be negative, so x ≠ - 33/2

Therefore:

$\small\boxed{\sf{ \red{x = 16}}}$

Breadth of the rectangle = x = 16 m

Length of the rectangle:

$\implies \sf 2x + 1$

$\implies \sf (2 × 16 + 1)$

$\implies \sf 32 + 1$

$\implies \sf 33 cm$

Hence, The length and the breadth of the plot is 33 cm and 16 cm.