Question

the legs of a right triangle are in the ratio of 3:4and its area is1014cm^. Find the hypotenuse​

Answer 1

Hypotenuse = 65 cm

Step-by-step explanation:

Let,

The legs of a right triangle are = 3x (side I)

The legs of a right triangle are = 4x (side II)

Area of triangle = 1014 cm²

So,

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

➙ 1/2 × 3x × 4x = 1014

➙ 0.5 × 12x² = 1014

➙ 6x² = 1014

➙ x² = 1014 / 6

➙ x² = 169

➙ $x \: = \sqrt{169}$

➙x = 13

Hence,

The legs of a right triangle are = 3x (side I)

➙ 3 × 13 = 39 cm

The legs of a right triangle are = 4x (side II)

➙ 4 × 13 = 52 cm.

We know that,

Hypotenuse² = Prependicular² + Base²

➙ Hypotenuse² = 39² + 52²

➙ Hypotenuse² = 1521 + 2704

➙ $Hypotenuse \: \: = \: \: \sqrt{4225}$

➙ Hypotenuse = 65 cm

Answer 2

Given:-

• area of traingle = 1014cm²

• ratio of base and heigth = 3:4

To find:-

• Hypotenuse = ?

Solution:-

Let the leg of traingle be x

then the base will be 3x and heigth will be 4x

We know that,

⇒Area of triangle = 1/2×base × heigth

⇒1014cm² = 1/2 × 3x ×4x

⇒1014 = 6x²

⇒x² = 169

⇒x =√169

⇒x = 13cm

⇒Base = 3x = 3×13 = 39

⇒Height = 4x = 4×13 = 52

As we know that,

⇒(hypotenuse)² = (height)² + (base)²

⇒(hypotenuse)² = 39² + 52²

⇒(hypotenuse)² = 1521 + 2704

⇒hypotenuse = √4225

⇒hypotenuse = 65cm

Hope its help uh❤