Question

If a line segment 45cm long is divided in the ratio 4:5, what is the length of longer part?​

Answer 1

Answer:

the ratio is 4:5

let the common multiple be x, then;

4x + 5x =45

9x = 45

x = 5

as the common multiple is 5 then the respective length of two parts are

4x = 4×5 =20 cm

5x = 5×5 =25 cm

therefore length of longer pat is 25cm

Answer 2

$\underline{ \underline{ \Large \sf { \pink{Answer:}} } }$

• Length of longer part = 25 cm

$\underline{ \underline{ \Large \sf { \pink{Given:}} } }$

• Line segment 45cm long is divided in the ratio 4:5.

$\underline{ \underline{ \Large \sf { \pink{To \: calculate:}} } }$

• Length of longer part.

$\underline{ \underline{ \Large \sf { \pink{Calculation:}} } }$

Here, we are provided that a line segment of length 45 cm is divided into two parts. Two parts are in ratio 4:5. We have to find out the length of longer part.

✰ In order to find the length of longer part, we'll assume the two parts as 4x & 5x first, where x is the constant natural number. Then, we'll find the measure of both parts by forming a suitable algebraic equation. By solving that equation, we'll get the value of x and shall find the measure of both parts. After that, we'll compare both parts to find which one is longer between the two parts.In this way,we'll get our answer.

⠀⠀⠀⠀⠀_____________

Let the length of the two parts be 4x and 5x.

According to the question,as 45 cm long line segment is divided into two parts ; so the sum of the two parts is equivalent to 45 cm.

$\longmapsto \rm { First \: Part + Second\: Part = 45 \: cm}$

$\longmapsto \rm { 4x + 5x= 45 } \\ \\ \\ \longmapsto \rm { 9x= 45 }\\ \\ \\ \longmapsto \rm {x= \dfrac{45}{9} } \\ \\ \\ \longmapsto \boxed{\pmb{ \rm \red { x= 5}} }$

Henceforth,

• First part = 4x

$\longmapsto \rm { First \: part = 4(5) \: cm} \\ \\ \\ \longmapsto \boxed{\pmb{ \rm \red { First \: part = 20 \: cm}} }$

Also,

• Second part = 5x

$\longmapsto \rm { Second \: part = 5(5) \: cm} \\ \\ \\ \longmapsto \boxed{\pmb{ \rm \red { Second \: part = 25 \: cm}} }$

So, it is clear that

• Second part > First part as 25 cm > 20 cm

Therefore,

$\longmapsto$ The length of longer part is $\pmb { \mathfrak \gray{25 \: cm}}$.