Question

The legs of a right triangle are in the ratio 3:4 and it's area is 1014 cm square. Find it's hypotenuse..​

Answer 1

$\huge\mathbb{SOLUTION:-}$

Given :-

The two legs of right triangle

To Find

We have to find the hypotenuse

$\bf\underline{According\:to\: Question:-}$

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

• let the two legs be x
• Then it's 3x and 4x

$\tt\rightarrow Area_\triangle=\frac{1}{2}\times 3x\times 4x\\ \\ \tt\rightarrow 1014=\frac{1}{\cancel2}\times cancel{12}x{}^{2}\\ \\ \tt\rightarrow 1014=6x{}^{2}\\ \\ \tt\rightarrow \cancel{\frac{1014}{6}}=x{}^{2}\\ \\ \tt\rightarrow 169=x{}^{2}\\ \\ \tt\longrightarrow \sqrt{169}=x\\ \\ \tt \implies x=13cm$

• The value of legs is 13×3=39cm
• 13×4=52cm

Now we have to find the hypotenuse of triangle

$\sf hypotenuse {}^{2}=base{}^{2}+altitude {}^{2}\\ \\ \tt hypotenuse {}^{2}=39{}^{2}+52{}^{2}\\ \\ \tt hypotenuse =\sqrt{1521+2704}\\ \\ \tt hypotenuse=\sqrt{4225}\\ \\ \tt\implies hypotenuse=65$

The hypotenuse of right triangle is 65cm

#BAL

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