Question

The sides of a right triangle are in the ratio 4:3 and its are is 726 cm². find its hypotenuse​

Answer 1

Answer:

Let the 2 legs be 4x and 3x.

Given, Area = 4056 cm²

therefore , 4056 = 1/2 × 4x × 3x

= 6x²

676 = x²

x = √676 = 26.

therefore the two sides:- 4x = 26 × 4 = 104cm

3x = 3 × 26 = 78cm

hypotenuse:- √104² + 78².

=130 cm.........

Answer 2

$\huge{{\huge{\boxed{\huge{\red\star\mathfrak\purple{\large{\underline{\underline{ Answer! }}}}}}}}}$

$\textsf{Let the common ratio be x}$

$\textsf{Base= 4x and perpendicular= 3x}$

Area of right triangle= $\bold{\frac{1}{2}× base× Height}$

$\bold{726= \bold{\frac{1}{2}}× 4x×3x}$

$\bold{726= \bold{\frac{1}{2}}×12x}$

$\textsf{726=6x}$

$\bold{x = \frac{726}{6} }$

$\bold {x = 121}$

$\bold{H^2= B^2+P^2}$

$\implies\bold{H^2= 4x+3x}$

H²= 7× 121

$\huge \boxed{ \underline{ \underline{\bold \star \red{\mathfrak{h {}^{2} = 847}}}}}$