## the legs of a right Triangle are in ratio 3 : 4 and its area is is 101 4 CM square. Find its hypotenuse​

Question

the legs of a right Triangle are in ratio 3 : 4 and its area is is 101 4 CM square. Find its hypotenuse​

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1 month 2021-08-17T05:38:11+00:00 2 Answers 0 views 0

1. Figure :- Refers to the attachment ✴ The legs of a right triangle are in ratio 3 : 4 and its area is is 1014 cm². Find its hypotenuse. ➡ The hypotenuse of Triangle is 65 cm. ## Given :-

• The legs of a right triangle are in ratio 3 : 4.
• The area of triangle is 1014 cm².

## To Find :-

• The hypotenuse of Triangle.

## Calculation :-

Let the leg of the triangle be x

So it’s sides 3:4 are equal to 3x and 4x .

According to the question,

We know the, Area of right angle triangle = ×base×hieght.

➝ 1014 = × 3x × 4x

➝ 1014 × 2 = 3x × 4x

➝ 2028 = 12x² = x²

➝ x² = ➝ x² = 169

➝ x = x = 13 cm

Using x finding the sides of triangle,

• 3x = 3×13 = 39
• 4x = 4×13 = 52

Here , We have a right triangle,applying Pythagoras theorem.

Pythagoras theorem states the sum of the square of two sides namely, perpendicular & base is equals to the square of its hypotenuse. Hypotenuse ² = P² + B²

➠ Hypotaneuse² = 39² + 52²

➠ Hypotaneuse² = (39×39) + (52×52)

➠ Hypotaneuse² = 1521 + 2704

➠Hypotaneuse = Hypotaneuse = 65 cm.

Hence, The hypotenuse of the triangle is 65 cm.

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2. Correct Question:

The length of two short sides of a right Triangle is in ratio 3:4 and its area is 1014 CM square. Find its hypotenuse. Solution:-

Given:

• The ratio of two short sides of the right triangle is 3:4
• The area of the right-angled triangle is 1014 cm sq.

Let, the side i.e Base be 3x cm

And Perpendicular (height) be 4x cm

• Area of the triangle = 1014 cm sq.        ∴ x = 13

So, Base = 3x = 39cm

And Perpendicular(height) = 4x = 52cm So, by using Pythagoras theorem, ⇒ Hypotenuse² = (39)² + (52)²

⇒ Hypotenuse² = 1521 + 2704

⇒ Hypotenuse² = 4225

⇒ Hypotenuse = ⇒ Hypotenuse = 65cm

Hence,

The Hypotenuse of the right-angled triangle is 65cm.