Question

The legs of a right triangle are in the ratio of 3:4 and its area is 1014 sq.cm. Find

its hypotenuse.​

Answer 1

Answer:

Let it's leg be 3x and 4x. Then,

according to question,

Area of right angle triangle = 1/2 × 3x × 4x

1,014 = 6x^2

1,014/6 = x^2

√169 = x

13 cm = x

Hence, first side = 3×13 = 39 cm

second side = 4×13 = 52 cm.

We know that

H^2 = P^2 + B^2

H^2 = 39^2 + 52^2

H^2 = 1521 + 2704

H = √4225

H = 65 cm.

Hence, the hypotenuse is 65 cm.

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Answer 2

Let the legs of the right angled triangle be 3x and 4x.

Now,

$\purple{\sf{Area \: of \: a \: triangle = \dfrac{1}{2} \times Base \times Height}}$

$\leadsto \: \sf{1014=\dfrac{1}{2} (3x) (4x)}$

$\Rightarrow \: \sf{1014 = 6x^{2} }$

$\Rightarrow \: \sf{x^{2} = \dfrac{1014}{6} }$

$\sf{\Rightarrow \: x^{2} = 169}$

$\to \: \sf{x = \sqrt{169} }\\\\\\\therefore \boxed{\bf{x = 13\: cm}}$

Legs of the right triangle are:

• 3x = 3(13) = 39 cm
• 4x = 4(13) = 52 cm

By Pythagoras theorem,

(Hypotenuse)² = (39)² + (52)²

→ (Hypotenuse)² = 1521 + 2704

→ (Hypotenuse)² = 4225

→ (Hypotenuse)² = √4225

∴ Hypotenuse = 65 cm