Question

Find the area of a right triangle with hypotenuse 50 cm and altitude 40 cm.​

Answer 1

GIVEN:

• Hypotenuse = 50 cm
• Altitude = 40 cm

TO FIND:

• What is the area of the triangle ?

SOLUTION:

Let the base of the triangle be 'b' cm

To find the base of the triangle, we use the Pythagoras theorem:-

$\large{\boxed{\bf{\star \: Hypotenuse^2 = base^2 + perpendicular^2 \: \star}}}$

According to question:-

➸ (50)² = b² + (40)²

➸ 2500 = b² + 1600

➸ 2500 –1600 = b²

➸ 900 = b²

➸ $\sf{\sqrt{900}}$ = b

❮ 30 cm = b ❯

We know that, the formula for finding the area of triangle is:-

$\large{\boxed{\bf{\star \: AREA = \dfrac{1}{2} \times BASE \times HEIGHT \: \star}}}$

On putting the given values in the formula, we get

➸ A = $\sf{\dfrac{1}{2}}$ $\times$ 30 $\times$ 40

➸ A = 15 $\times$ 40

❮ AREA = 600 cm² ❯

❝ Hence, the area of triangle is 600 cm² ❞

______________________

Answer 2

A N S W E R :

• The area of the triangle is 600m²

Given :

• The hypotenuse of a triangle is 50cm

• The altitude of the triangle is 40cm

To find :

• Find area of the triangle ?

Solution :

• Now, as we have, the measurements of the altitude and the hypotenuse of the triangle let's usse pythagoras therom to find the measurements of its base and then we can find the area of the triangle

Formula Used :

Pythagoras Theorem :

★ [(Hypotenuse)² = (Side)² + (Base)²]

Concept Used :

=> (H)² = (S)² + (B)²

=> (50m)² = (40m)² + (Base)²

=> 2500m² = 1600m² + (Base)²

=> (Base)² = 2500m² - 1600m²

=> (Base)² = 900m²

=> Base = √900m²

=> Base = 30m

Henceforth,

• The base of the triangle is 30m.

Now, We have,

• Let's Find the area of the triangle

As we know that,

★ [Area_(triangle) = 1/2 × base × height]

• Substituting the values,

=> Area = 1/2 × Base × Height

=> Area = 1/2 × 30m × 40m

=> Area = 15m × 40m

=> Area = 600m²

Hence,

• The area of the triangle is 600m².