Question

find the area of rectangular plot one side of which measure 12 cm and diagonal is 37 m

Answer 1

Let length be xcm
then,
${x}^{2} + {12}^{2} = {37}^{2}$

${x}^{2} + 144 = 1369$
${x }^{2} = 1369 - 144$
x=35 cm
area = 35×12
= 420

Answer 2

Given:- If a diagonal of a rectangle is 37 cm and one side is 12 cm .

To Find:- The other side .

Solution :- Given that If a diagonal of a rectangle is 37 cm and one side is 12 cm .

So , the Figure would be something like this ; [ If LaTeX doesn't work on app see the attachment or refer to website ]

$\setlength{\unitlength}{1 cm}\begin{picture}(12,8)\thicklines\put(0,0){\line(6,5){5}}\put(5,4.15){\line(0, - 1){4.15}}\put(5,0){\line(-1,0){5}}\put(0,4.15){\line(1,0){5}}\put(0,4.149){\line(0,-1){4.149}}\put(0,-0.3){ \tt A }\put(5,-0.3){ \tt B }\put(5,4.46){ \tt C }\put(0,4.46){ \tt D }\put(4.8,0){\line(0,1){0.2}}\put(4.8,0.2){\line(1,0){0.2}} \put(5.3,2){ \sf 12 cm }\put(1.5,2.2){ \sf 37 cm }\end{picture}$

→ So , In ∆ ABC ;

⇒ AC² = AB² + BC²

⇒ ( 37 cm )² = AB² + ( 12 cm )²

⇒ 1369cm² = AB² + 144cm².

⇒ AB² = 1369 cm² - 144 cm²

⇒ AB² = 1225 cm².

⇒ AB = √ 1225 cm²

⇒ AB = 35 cm .

→Hence the value of other side is 35 m .

Now , area = ( lenght × breadth )

= 35 cm × 12 cm

= 420 cm²

★ Hence the area is 420 cm² ★

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