Question

[ HUNDRED POINTS]Two adjacent sides of rectangle are 5 x+6 and 2 x + 66. Find its area if its perimeter is 186 cm (answer in square centimetre please)

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

$\blacksquare \:$ RECTANGLE

A rectangle is a quadrilateral where

• all angles are 90°
• opposite sides are equal
• Opposite sides are parallel
• Two sides are greater than the other two

$\blacksquare$FORMULA FOR PERIMETER & AREA

Let Length of the rectangle = x unit

Width of the rectangle = y unit

Then Perimeter = 2(x+y) unit

Area = xy sq unit

$\blacksquare \:$CALCULATION

Since the area to be determined in Square Centimeters

So the unit of side & perimeter must be centimeter

Two adjacent sides of rectangle are 5x+6 cm and

2x + 66 cm

So perimeter

$= \:2 \{ (5x + 6) + (2x + 66) \} = 2(7x + 72) \: \: \: cm$

It is given that perimeter is 186 cm

So

$2(7x + 72) = 186$

$\implies \: 7x + 72 = 93$

$\implies \: 7x = 21$

$\therefore \: x \: = 3$

Hence Two adjacent sides of rectangle are (15+6) = 21 cm and (6 + 66 ) = 72 cm

Hence the required area

$= 72 \times 21 \: \: \: \: sq \: cm$

$= 1512 \: \: \: sq \: cm$

Answer 2

Answer:

A rectangle is a quadrilateral where

all angles are 90°

opposite sides are equal

Opposite sides are parallel

Two sides are greater than the other two

■ FORMULA FOR PERIMETER & AREA

Let Length of the rectangle = x unit

Width of the rectangle = y unit

Then Perimeter = 2(x+y) unit

Area = xy sq unit

■ CALCULATION

Since the area to be determined in Square Centimeters

So the unit of side & perimeter must be centimeter

Two adjacent sides of rectangle are 5x+6 cm and

2x + 66 cm

So perimeter

$= \:2 \{ (5x + 6) + (2x + 66) \} = 2(7x + 72) \: \: \: cm=2{(5x+6)+(2x+66)}=2(7x+72)cm$

It is given that perimeter is 186 cm

So

$2(7x + 72) = 1862(7x+72)=186 \\\\</p><p></p><p>\implies \: 7x + 72 = 93⟹7x+72=93 \\\\</p><p></p><p>\implies \: 7x = 21⟹7x=21 \\\\</p><p></p><p>\therefore \: x \: = 3∴x=3$

Hence Two adjacent sides of rectangle are (15+6) = 21 cm and (6 + 66 ) = 72 cm

Hence the required area

$= 72 \times 21 \: \: \: \: sq \: cm=72×21sqcm$

$= 1512 \: \: \: sq \: cm=1512sqcm$