Question

5) The area of a right triangle is 6 cm². If one of the
sides containing the right angle is 4 cm, find the
length of its hypotenuse.​

Answer 1

Answer:

5 cm

Step-by-step explanation:

Area of right angled triangle = 1/2* base * height

given that,

                  base= 4cm

∴ 6cm² = 1/2 * 4cm * height

   height = (2 * 6)/4 cm = 12/4 cm = 3 cm

∴ According to pythagorus theorum

 (3cm)² + (4cm)² = hypotenuse²

hypotenuse²=9cm²+16cm²

hypotenuse² = 25 cm²    

hypotenuse = 5 cm

Answer 2

$\mathfrak{\large{\underline{\underline{Given:-}}}}$

area of right triangle = 6 cm^2

base = 4 cm

$\mathfrak{\large{\underline{\underline{To find:-}}}}$

Length of hypotenuse = ?

$\mathfrak{\large{\underline{\underline{Solution:-}}}}$

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

$\implies$ $\bold{6 = \frac{1}{2} \times 4 \times height }$

$\implies$ $\bold{6 = 2 × height }$

$\implies$ $\bold{height = 3 cm }$

Now,use Pythagorean theorem

★ $\bold{h = \sqrt{ {b}^{2} + {p}^{2} } }$

$\implies$ $\bold{h = \sqrt{ {4}^{2} + {3}^{2} } }$

$\implies$ $\bold{h =\sqrt{25} }$$\implies$ $\bold{h = 5 cm }$

hence, the length of hypotenuse is 5 cm.