Question

8. The legs of a right triangle are in the ratio 3 : 4 and its area is 1014 cm. Find the lengths of
its legs.
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Answer 1

Answer:

Given :-

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

To Find :-

• What is the length of its legs.

Solution :-

Let, the first leg be 3x

And, the second leg be 4x

According to the question,

⇒ ½ × 3x × 4x = 1014

⇒ ½ × 12x² = 1014

⇒ 6x² = 1014

⇒ x² = 1014/6

⇒ x² = 169

⇒ x = √169

➠ x = 13

Hence, the required legs are,

✧ First leg = 3x = 3(13) = 39 cm

✧ Second leg = 4(13) = 52 cm

∴ The length of its legs are 39 cm and 52 cm respectively.

Answer 2

Answer :-

Given :-

• Ratio of the legs of right triangle = 3 : 4

• Area of the right triangle = 1014cm²

To Find :-

• Length of the legs of right triangle

Solution :-

Let the legs be 3x and 4x

According to the question,

Area of the right triangle = 1/2 × length of it's legs of the triangle

By substituting values,

⇒ 1/2 × 3x × 4x = 1014cm²

⇒ 1/2× 12x² = 1014cm²

⇒ 6x² = 1014cm²

⇒ x² = 1014/6

⇒ x² = 169

⇒ x =√169

➥ x = 13

Therefore, The length of the legs be

• 3x = 3 × 13 = 39cm
• 4x = 4 × 13 = 52cm

Hence, The lengths of legs of the right triangle are 39cm and 52cm