Question

the length and width of a rectangle are in the ratio 5 :3. find dimensions of the rectangle if the perimeter is 112 CM​

Answer 1

$\huge\bold{\mathtt{Question⇒}}$

The length and width of a rectangle are in the ratio $5:3.$ find dimensions of the rectangle if the perimeter is $112$ cm.

$\huge\bold{\mathtt{Given⇒}}$

• The length and width of a rectangle are in the ratio $5:3.$

• The perimeter is $112$ cm.

$\huge\bold{\mathtt{To\:find⇒}}$

It's dimensions.

$\huge\bold{\mathtt{Solution⇒}}$

Let the length be $5x$ cm and width be $3x$ cm.

Perimeter = $112$ cm

We know that:

Perimeter = 2(Length+Breadth)

So, we can say-

$2(5x + 3x) = 112$

$➳\:2 × 8x = 112$

$➳\:16x = 112$

$➳\:x = {\frac{112}{16}}$

$➳\:x = 7$

$\huge\bold{\mathtt{Hence⇒}}$

$x = 7$

Length = $5x$ cm = $(5 × 7)$ cm = $35$ cm

Breadth = $3x$ cm = $(3 × 7)$ cm = $21$ cm

$\huge\bold{\mathtt{Therefore⇒}}$

Its length is $35$ cm and breadth is $21$ cm.

$\huge\bold{\mathtt{Done}}$

$\large\bold{\mathtt{Hope\:this\:helps\:you.}}$

$\large\bold{\mathtt{Have\:a\:nice\:day.}}$