Question

⚡Qᥙᥱ⳽tioᥒ :

★The perimeter of a rectangle is 70 cm its length exceeds its breadth 5 cm.Find the area of the rectangle!!

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Answer 1

This is your ans I hope it helps you

Answer 2

${\underline{\large{\pmb{\frak{Given : }}}}}$

★ The perimeter of a rectangle is 70 cm.

★ The length of the rectangle exceeds its breadth 5 cm

${\underline{\large{\pmb{\frak{To\; Find : }}}}}$

★ The measure of  the area of the rectangle

${\underline{\large{\pmb{\frak{Understanding \; the \; question : }}}}}$

☀️ Concept : Here we'have been said that the perimeter of a rectangle is 70cm and the length of it exceeds its breadth by 5cm and asked to find the area of it. Now as the breadth of the rectangle is undefined and the length measure 5cm more that the breadth

❍ Let's assign a suitable variable to the breadth and denote the length as 5 more than it. As we have the measure of the perimeter let's find the dimensions using it and then find the area applying suitable formulae.

${\underline{\large{\pmb{\frak{Using \; Concepts: }}}}}$

✪ Formula to find the perimeter of a rectangle :

 $\tt Perimeter = 2(Lenght + Breadth)$

✪ Formula to find the area of a rectangle :

$\tt Area \; of \; a \; rectangle = Length \times Breadth$

${\underline{\large{\pmb{\sf{RequirEd \;Solution : }}}}}$

★ The area of the rectangle is 300cm^2

${\underline{\large{\pmb{\frak{Full \; solution : }}}}}$

~ Now as we know that the perimeter is 70cm , the dimensions are unknown let's denote the breadth as x and the length as x + 5cm and let's find them by substituting them in the formula given below.

✰ Formula,

• Perimeter = 2 ( length + Breadth )

✰ Here,

• Length = x + 5cm
• Bradth = x
• Perimeter = 70cm

~ Substituting them we get,

${: \implies}\sf \; Perimeter = 2 ( Lenght + Breadth )$

${: \implies}\sf 70cm = 2( x + 5cm + x )$

${: \implies}\sf 70cm = 2x + 10cm + 2x$

${: \implies}\sf 70cm = 4x + 10cm$

${: \implies}\sf 4x = 70cm - 10cm$

${: \implies}\sf 4x = 60cm$

${: \implies}\sf x = \dfrac{60cm}{4}$

${: \implies}\sf x = 15cm$

~ Now let's find the dimensions of them

${: \implies}\sf Breadth = 1x = 1(15cm) = 15cm$

${: \implies}\sf Lenght = x + 5cm = (15cm) + 5cm = 20cm$

• Henceforth the measure of the length and breadth are 20cm and 25cm respctively

~ Now, let's find the area of the rectangle substituting the values of the length and breadth in the formula mentioned below

✰ Formula :

• Area of the rectangle = Length × Breadth

✰ Here,

• Length = 20cm
• Breadth = 15cm

~ Substituting the measures of the length and breadth in the formula in the formula we get,

${: \implies}\sf Area = L \times B$

${: \implies}\sf Area = 20cm \times 15cm$

${: \implies}\sf Area = 300cm^{2}$

• Henceforth thr area of the rectangle is 300cm^2

${\underline{\large{\pmb{\frak{Additional\; Information : }}}}}$

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;{ \leadsto} \tt Perimeter \; of \; a square = 4 \times side$

$\;\;\;\;\;\;\;\;\;\;\;\;\;\; {\leadsto }\tt Area \; of \; a \; square \; = Side \times Side$

$\;\;\;\;\;\;\;\;\;\;\;\;\;\; {\leadsto} \tt Area \; of \; a \; triangle = \frac{1}{2} \times base \times hieght$

$\;\;\;\;\;\;\;\;\;\;\;\;\;\; {\leadsto} \tt Area \; of \; a \; rhombus = d_1 \times d_2 \times \frac{1}{2}$

$\;\;\;\;\;\;\;\;\;\;\;\;\;\; {\leadsto} \tt Area \; of \; a \; parallelogram = Base \times hieght$

${\bigstar \; {\underline{\purple{\underline{\sf{Rectangle...}}}}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\bf\large 20 cm}\multiput(-1.4,1.4)(6.8,0){2}{\bf\large 15 cm}\end{picture}$

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