Question

the area of a triangle is equal to the area of a square whose each side measure 10 cm.find the length of the side of a triangle corresponding to the altitude measuring 5m​

Answer 1

$\huge\mathbb{SOLUTION:-}$

• Given that the area of triangle is equal to the area if square

• and the side of square is 10cm

• First find the area of square

$\boxed{\sf{Area\:of \: Square=side {}^{2}}}$

$\sf\implies Area\:of\:square= (10){}^{2}\\ \\ \sf\implies Area\:of\: square=100cm{}^{2}$

• Now we have to find the base of triangle
• and the altitude is given

$\boxed{\sf{Area\:of\: triangle=\frac{1}{2}\times base\times height}}$

$\sf\underline{ Area\:of\: triangle=100cm{}^{2}}$

• Let the base of triangle be x

• and height=5cm

$\sf\implies 100=\frac{1}{2}\times x\times 5\\ \\ \sf\implies 100\times 2=5x\\ \\ \sf\implies \cancel{\frac{200}{5}}=x\\ \\ \sf\implies 40=x\\ \\ \sf\implies x=40cm$

$\underline{\boxed{\sf{Side\:of\: triangle=40cm}}}$

Answer 2

Answer:

$\small\underline\textsf{\orange{Side} \blue{of }\red{triangle} = \purple{40cm}}$

$\large\underline\textsf{To Find }$

$\small\textsf{the\: length \:of \:the\: side \:of \:a\: triangle }$

$\huge\underline\textsf{Explantion:- }$

$\leadsto\bf area \: of \: square = (10) {}^{2}$

$\leadsto\bf area \: of \: square = 100cm {}^{2}$

$\huge\underline\textsf{ Formula\: Used}$

$\boxed{\bf\red{Area \: of \: Base = \frac{1}{2} \times base \times Hieght}}$

$\implies\bf area \: of \: triangle = 100cm {}^{2}$

$\small\underline\textsf{ suppose the base of triangle \red{be Y}}$

$\small\underline\textsf{hieght=5}$

$\rule{300}{2}$

$\leadsto\sf100 = \frac{1}{2} \times y \times 5$

$\leadsto\sf 100 \times 2 = 5y$

$\leadsto\sf \frac{\cancel{200}}{\cancel5}$

$\leadsto\sf40 = y$

$\leadsto\sf y = 40cm$

$\underline{\underline{\underline{\boxed{\boxed{\boxed{\bf{ The \:side\: of \:Triangle \:= 40cm}}}}}}}$