Question

the side of a rectangle are in the ratio of 4:5 and its perimeter is 90 cm . find the dimensions of the rectangle and hence its area .​

Answer 1

Answer:

let the ratios be x.

hence,per=2(l+b)=2(4x+5x)=2(9x)=18x

90=18x

x=5

hence,l=4x=4×5=20

b=5x=5×5=25

hence,area=l×b=20×25=500

pls mark me as brainliest

Answer 2

$\bf \: { \underline{Given} \: :}$ ↴

$\sf \: The \: ratio \: of \: sides \: of \: the \: Rectangle \: = \: 4 : 5$

$\sf \: Perimeter \: of \: Rectangle \: = \: 90 \: cm$

$\bf \: { \underline{To \: find } \: : }$ ↴

$\sf \: The \: Measures \: of \: the \: sides \: of \: the \: Rectangle \: and \: It's \: area.$

$\bf \: { \star \: \underline{So, \: Let's \: Start } \: \star}$

$\sf \: Consider \: one \: side \: as \: 4x$

$\sf \: Second \: as \: 5x$

$\purple{ \bigstar} \: \purple{\boxed{ \purple{\sf{2(Length + Breadth)}}}} \: \purple{ \bigstar}$

$\sf \longrightarrow \: 2(4x + 5x) = 90$

$\sf \: \longrightarrow \: 8x + 10x = 90$

$\sf{\longrightarrow} \:18x = 90$

$\sf{ \longrightarrow} \:x \: = \: \dfrac{90}{18}$

$\sf{\longrightarrow} \: x \: = \: 5$

$\bf \star \: Value \: of \: 4x :$

$\sf \rightarrow4 \: \times 5 \: = \: 20$

$\bf \star \: Value \: of \: 5x :$

$\sf \rightarrow5\: \times 5 \: = \: 25$

$\sf \red{Hence, \: the \: Sides \: of \: a \: Rectangle \: are \: 20 \: and \: 25. }$

______________________________________

$\sf \: Now, \: we \: will \: find \: the \: area \: of \: the \: rectangle.$

$\purple{\bigstar }\: \boxed{ \purple{\sf{Area = Length \times Breadth}}} \: \purple{ \bigstar}$

$\sf{\longrightarrow} \: 25 \: \times \: 20$

$\sf{\longrightarrow} \: 500$

$\sf \: \red{The \: area \: of \: the \: Rectangle \: is \: 500 \: sq.unit.}$