Question

The perimeter of a rectangle is 17 cm . If its width is 3 ¾

cm, then find its length.​

Answer 1

GIVEN:

Perimeter of rectangle = 17 cm

Width = 3¾ cm = 15/4 cm

SOLUTION:

We know that perimeter of a rectangle is 2(Length + Width)

∴ perimeter = 2[length + (15/4)]

==> 17 = 2[length + (15/4)]

==> 17 = 2(length) + 30/4

==> 2(length) = 17 - 30/4

==> length = (17 - 7.5)/2

==> length = 9.5/2 = 4.75

Required length of rectangle is 4.75 cm

Answer 2

Answer:

Given:-

The perimeter of a rectangle is 17 cm, if it's width is $3 \ \dfrac{3}{4}$ cm, then find its length.

To Find:-

The length.

Note:-

●》Here, we will find length by the formula of Perimeter of rectangle i.e. Perimeter of rectangle = 2 × ( Length + Width ).

●》For finding unknown value, known value needs to transposed from its side to another and signs are also changed or not ( signs are not changed in multiple and divisional value ). For example - Positive becomes Negative, Multiple becomes Divisional.

Solution:-

$\huge\red{Perimeter \ \ of \ \ rectangle = 17 cm}$

$\huge\red{Width = 3 \ \dfrac{3}{4} cm}$

$\huge\red{\ \ \ \ Length = ?, Let \ \ it \ \ be \ \ "x"}$

☆ According to note first point~

▪︎$Perimeter \ \ of \ \ rectangle = 2 × ( Length + Width )$

▪︎$17 cm = 2 × ( x + 3 \ \dfrac{3}{4} cm )$

▪︎$17 cm = 2 × ( x + \dfrac{15}{4} cm )$

▪︎$17 cm = 2 × x + 2 × \dfrac{15}{4} cm$

▪︎$17 cm = 2x + \dfrac{30}{4} cm$

☆ According to note second point ( transposing )~

▪︎$17 cm - \dfrac{30}{4} cm = 2x$

☆ L.C.M = 4~

▪︎$17 cm × \frac{4}{4} - \dfrac{30}{4} cm × \frac{1}{1} = 2x$

▪︎$\dfrac{68}{4} cm - \dfrac{30}{4} cm = 2x$

▪︎$\dfrac{38}{4} cm = 2x$

▪︎$\dfrac{38}{\frac{4}{2}} cm = x$

▪︎$\dfrac{38}{4 × 2} cm = x$

▪︎$\dfrac{38}{8} cm = x$

☆ After dividing~

▪︎$\dfrac{19}{4} cm = x$

☆ Decimal Point~

▪︎$4.75 cm = x$

$\huge\pink{Length = x => \dfrac{19}{4} cm \ \ or \ \ 4.75 cm}$

Checking:-

♤ Let's check that Perimeter of rectangle = 2 × ( Length + Width ) or not.

• $Perimeter \ \ of \ \ rectangle = 2 × ( Length + Width ) \implies ?$

• $17 cm = 2 × ( \dfrac{19}{4} cm + 3 \ \dfrac{3}{4} cm ) \implies ?$

• $17 cm = 2 × ( \dfrac{19}{4} cm + \dfrac{15}{4} cm ) \implies ?$

• $17 cm = 2 × \dfrac{34}{4} cm \implies ?$

• $17 cm = \dfrac{68}{4} cm \implies ?$

• $17 cm = 17 cm \implies ✔$

$\huge\green{Hence, Proved : Length = \dfrac{19}{4} cm \ \ or \ \ 4.75 cm}$

Answer:-

Hence, the value of Length = $\dfrac{19}{4} cm$ or 4.75 cm.