Question

the length of a rectangular garden is 4 yards more than its width. the are of the garden is 60 square yards. find the dimensions of the garden

Answer 1

$\huge {\bold {\red {Answer}}}$

Length = 10 yards

Breadth = 6 yards

$\huge {\bold {\red {Explanation}}}$

Let breadth = x yards

And length = (x + 4) yards

Given area = 60 yards²

According to the question,

Area = Length × Breadth

=> 60 = (x + 4) × x

=> 60 = x² + 4x

=> x² + 4x - 60 = 0

=> x² + 10x - 6x - 60 = 0

=> x (x + 10) - 6 (x + 10) = 0

=> (x - 6) (x + 10) = 0

=> x = 6 or x = -10

Since dimensions can't be negative, therefore

x = 6.

Hence,

Length = 6 + 4 = 10 yards

Breadth = 6 yards

$\huge {\red {\bold {Thank You}}}$

Answer 2

$\underline{ \underline{ \boxed{ \large{ \frak{ \blue{Question}}}}}}$

The length of a rectangular garden is 4 yards more than it's width. the area of the garden is 60 square yards. find the dimensions of garden.

$\underline{ \underline{ \boxed{ \large{ \frak { \green{Solution}}}}}}$

Let,

length of garden, l = x yards

then,

breadth of garden, b = x - 4 yards

given,

area of garden = 60 sq. yards

as we know,

length × breadth = area of garden

so,

$\tt \: x(x - 4) = 60 \\ \\ \tt \: {x}^{2} - 4x - 60 = 0 \\ \\ \tt \: splitting \: the \: middle \: term \\ \\ \tt \: {x}^{2} - 10x + 6x - 60 = 0 \\ \\ \tt \: x(x - 10) + 6(x - 10) = 0 \\ \\ \tt \: (x + 6)(x - 10) = 0 \\ \\\tt here \: we \: get \\ \tt x = - 6 \\ \tt or \: x = 10$

since,

length cannot be negative

therefore

we will take

x = 10

so,

$\boxed{ \tt \: length = 10 \: yards}$

and

$\boxed{ \tt \: breadth = 10 - 4 = 6 \: yards}$