Question

"Half the perimeter of a rectangular garden whose length is 12 m more than its width is 60m. find the dimensions of the garden

Answer 1

Answer:

Length of whole garden =12m

Breadth of whole garden = 60m

perimeter of whole garden=l×b

=12×60=720

perimeter of half garden = perimeter of whole garden ×1/2

= 720 × 1/2

=360 m

so perimeter of half garden is 360m

Answer 2

Given:-

• Half the perimeter of a rectangular garden whose length is 12m more then its width, 60cm.

To find:-

• Dimensions of the garden

Solution:-

$\bold{\underline{\boxed{\sf{\red{\dag \; Perimeter \; of \; rectangle = 2(l + b)}}}}}$

∴ Half of perimeter = $\sf{ \dfrac{2(l + b)}{2}}$

$\implies \sf{Length + Breadth}$

Now,

Let's the breadth of rectangle be x m.

Therefore its length = (x + 12)m

Length + Breadth = 60m

x + (x + 12) = 60

2x + 12 = 60

2x = 60 - 12

2x = 48

x = $\sf{ \cancel{ \dfrac{48}{2}}}$

$\bold{\underline{\boxed{\sf{\blue{\dag \; x = 24m}}}}}$

★ Hence, dimensions of rectangular garden :-

• Length:- (x + 12) = 24 + 12 = 36m
• Breadth:- x = 24m

Verification:-

If half the perimeter of rectangular garden is 60m,

then full perimeter = 60 × 2 = 120m

Perimeter of rectangular garden according to formula,

$\implies \sf{2(36 + 24)}$

$\implies \sf{2 \times 60}$

$\implies \sf{120m}$

$\bold{\underline{\underline{\sf{\purple{\dag \; Hence \; Verified!}}}}}$

$\rule{200}{2}$