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

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a rectangle whose adjacent sides are in the ratio 7:5
• Perimeter of rectangle is 144 cm

To Find:

• We need to find all sides of rectangle

Solution:

Let The length of Rectangle = 7x

Breadth of Rectangle = 5x

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$\underline{\large{\blue{\mathfrak{According\:to\:the\:Question :}}}}$

$\hookrightarrow \boxed{\sf{\orange{ Perimeter = 2 (length + Breadth) }}}$

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

$\hookrightarrow \sf{ 7x + 5x = 72 }$

$\hookrightarrow \sf{ 12x = 72 }$

$\hookrightarrow \sf{ x = \dfrac{72}{12}}$

$\hookrightarrow \sf{ x = \cancel{\dfrac{72}{12}}}$

$\hookrightarrow \boxed{\sf{ x = 6 }}$

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Therefore:

$\implies$Length of Rectangle = 7x

$\implies 7 \times 6$

$\implies 42$

$\implies$Breadth of Rectangle = 5x

$\implies 5 \times 6$

$\implies 30$

$\boxed{\sf{\large\mathfrak\red{Length \: of \: Rectangle = 42 \: cm }}}$

$\boxed{\sf{\large\mathfrak\red{Breadth \: of \: Rectangle = 30 \: cm }}}$

Hence side of rectangle is 42, 30, 42 ,30

Answer 2

Let the sides be = 7x, 5x

Perimeter of rectangle = 2(l+b) = 144

=> 2(7x+5x) = 144

=> 12x = 72

=> x = 6

Thus the sides are = 42 units, 30 units