Question

The adjacent sides of a rectangle are in the ratio of 7:5 perimeter is 144 find the measure of each side

Answer 1

$\underline{ \underline{ \sf{Given}}}$

• The adjacent sides of a rectangle are in the ratio of 7:5 .

• Perimeter of rectangle is 144 .

$\underline { \underline { \sf{To \: find \: out }}}$

Find the measure of each side of rectangle?

$\underline { \underline {\sf{Formula \: used}}}$

$\boxed{ \sf{ Perimeter \: of \: rectangle = 2(l + b)}}$

$\underline{ \underline{ \sf{Solution}}}$

Let the length and breadth be 7x and 5x respectively.

Perimeter = 144 [ Given ]

According to the question,

${\sf{ Perimeter \: of \: rectangle = 2(l + b)}}$

$\sf { \star \: Putting \: the \: values \: of \: l \: and \: b} </p><p>$

$:\implies \sf{ 144 = 2(7x + 5x)}$

$: \implies \sf{144 = 14x + 10x}$

$: \implies \sf{144 = 24x}$

$: \implies \sf{x = \cancel\dfrac{144}{24} }$

$: \implies \sf{x = 6}$

Now,

★ Length = 7x

Putting the values of x,we get :

⇒ Length = 7 × 6

⇒ Length = 42 m

★ Breadth = 5x

Putting the values of x,we get :

⇒ Breadth = 5 × 6

⇒ Breadth = 30 m

Thus, Sides are 42 m,30 m ,42 m ,30 m .

Answer 2

$\huge{\underline{\pink{\tt{Answer:}}}}$

• Measurement of Each Side - 42m , 30m , 42m , 30m.

Given,

• The Adjacent sides of a Rectangle are in the Ratio of 7:5.
• Perimeter of Rectangle is 144 m.

To Find,

• Length of Rectangle
• Breadth of Rectangle

Solution :

$\longrightarrow$ Suppose the Common measurement of Length and Breadth be a

Therefore,

• The Length of Rectangle be 7a.
• The Breadth of Rectangle be 5a.

$\bigstar \large{\underline{\orange{\tt{According\:to\;the\:Question :}}}}$

We Know that :

$\longmapsto \boxed{\pink{\sf{Perimeter\:of\:Rectangle = 2(Length + Breadth)}}}$

So,Now Put the Value in this Formula :

$\longmapsto \sf{144 = 2(7a + 5a)}$

$\longmapsto \sf{144 = 2(12a)}$

$\longmapsto \sf{144 = 24a}$

$\longmapsto \sf{a = \dfrac{144}{24}}$

$\longmapsto \boxed{\sf{a =6}}$

Hence,

$\mapsto \underline{\boxed{\mathfrak{The\:Length\:of\:Rectangle = 7a = 7(6) = 42\:m}}}$

$\mapsto \maspto \underline{\boxed{\mathfrak{The\:Breadth\:of\:Rectangle = 5a = 5(6) = 30\:m}}}$

$\rule{200}2$