Question

a wire of lenght 86 cm is bent in the form of a rectangle such that it's lenght is 7cm more than its breadth.find the lenght and the breadth of the recatangle so formed

Answer 1

AnswEr :

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

A wire of length 86 cm is bent in the form of a rectangle such that it's length is 7 cm more than it's breadth.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The length and the breadth of the rectangle so formed.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Let the breadth of rectangle be r cm

Let the length of rectangle be (r+7) cm

Formula use :

$\bf{\boxed{\sf{Perimeter\:of\:rectangle=2(Length+Breadth)}}}}}$

A/q

$\mapsto\sf{86\:cm = 2[(R+7)+r]}\\\\\\\mapsto\sf{86\:cm=2(r+7+r)}\\\\\\\mapsto\sf{86\:cm=2(2r+7)}\\\\\\\mapsto\sf{86\:cm=4r+14\:cm}\\\\\\\mapsto\sf{4r=86\:cm-14\:cm}\\\\\\\mapsto\sf{4r=72\:cm}\\\\\\\mapsto\sf{r=\cancel{\dfrac{72}{4} }}\\\\\\\mapsto\sf{\pink{r=18\:cm}}$

Thus;

$\bf{\boxed{\sf{The\:length\:of\:the\:rectangle\:=(r+7)=18+7=\pink{25\:cm}}}}}\\\bf{\boxed{\sf{The\:breadth\:of\:the\:rectangle\:=r=\pink{18\:cm}}}}}}$

Answer 2

AnswEr:-

Length of rectangle formed = 25 cm

Breadth of rectangle formed = 18 cm

$\rule{200}{1}$

Given :-

• Length of wire = 86 cm
• Length of rectangle formed = Breadth + 7 cm

To find :-

• Length = ?
• Breadth = ?

Solution :-

As there is given length of wire which is bent to form a rectangle.So length of wire will be equal to perimeter of rectangle formed.

Let the breadth of rectangle formed = M cm. & length of rectangle formed =(M + 7) cm.

Now,we know,

$\bf{\dag}\:{\boxed{\sf{Perimeter_{rectangle} = 2(length + breadth) }}}$

$\scriptsize\sf {\_ \_ \_ \_ \_ \_\_(Put \: values:-)}$

$\twoheadrightarrow\sf 2(M + 7 + M) = 86 \\\\\twoheadrightarrow\sf 2(2M + 7) = 86 \\\\\twoheadrightarrow\sf 2M + 7 = 86/2 \\\\\twoheadrightarrow\sf 2M + 7 = 43 \\\\\twoheadrightarrow\sf 2M = 43 - 7 \\\\\twoheadrightarrow\sf 2M = 36 \\\\\twoheadrightarrow\sf M = 36/2 \\\\\twoheadrightarrow\large{\underline{\boxed{\sf\blue{M = 18 \: cm }}}}$

$\rule{100}{2}$

Dimensions:-

➩ Length = M + 7 = 18 + 7 = 25 cm

➩ Breadth = M = 18 cm

Therefore,

Length and breadth of rectangle = 25 cm & 18 cm respectively.