Question

if the ratio of the base and hypotenus of a right angled triangle 4:5 and the Perimeter of the triangle is 48 find its area​

Answer 1

${ \bf{ \underline{ \green{Required \: \: Solution :-}}}}$

★ Given :-

• Base : Hypotenuse = 4 : 5
• Perimeter of the triangle = 48 cm

★ To Find :-

• Area ?

★ Solútion :-

☯︎ Let the common term of ratio be 'x'

Now,

• Base = 4x
• Hypotenuse = 5x

Now, By using Pythagoras theorem :-

★ Hypotenuse² = Base² + Perpendicular² ★

Now substitute the values :-

↦ (AC)² = (AB)² + (BC)²

↦ (5x)² = (AB)² + (4x)²

↦ (AB)² = (5x)² - (4x)²

↦ (AB)² = (25x) - (16x)

↦ AB = √9x²

↦ AB = 3x

◆ We know that,

★ Perimeter = AB + BC + AC ★

Now, substitute the values :-

↦ Perimeter = 3x + 4x + 5x

↦ Perimeter = 12x

↦ Perimeter = 48 ------ ( Given )

↦ 12x = 48

↦ x = 48 / 12

↦ x = 4 cm

Now, Putting the values of x.

↦ Base = 4x = 4 × 4 = 16 cm

↦ Hypotenuse = 3x = 3 × 4 = 12 cm

◆ We also know that,

★ Area of triangle = 1 / 2 Base × height ★

Now, substitute the values :-

↦ Area of triangle = 1 / 2 16 × 12

↦ Area of triangle = 16 × 6

↦ Area of triangle = 96 cm²

■ Hence, the Area is 96 cm².

__________________________

Answer 2

$\large \bf\green{Required~Solution}$

$\{/bf{Given :-}}$

• Base : Hypotenuse = 4 : 5

• Perimeter of the triangle = 48 cm

To Find

• Area?

Solution

Let the common term of ratio be 'x'

Now,

• Base = 4x

• Hypotenuse = 5x

Now, by using pythagoras theorem :-

★ Hypotenuse² = Base² + Perpendicular² ★

Now substitute the values :-

➹ (AC)² = (AB)² + (BC)²

➹ (5x)² = (AB)² + (4x)²

➹ (AB)² = (5x)² - (4x)²

➹ (AB)² = (25x) - (16x)

➹ AB = √9x²

➹ AB = 3x

★ We know that,

★ Perimeter = AB + BC + AC ★

Now, substitute the values :-

➹ Perimeter = 3x + 4x + 5x

➹ Perimeter = 12x

➹ Perimeter = 48 ------ (Given)

➹ 12x = 48

➹ x = 48 / 12

➹ x = 4 cm

Now, Putting the values of x.

➹ Base = 4x = 4 × 4 = 16 cm

➹ Hypotenuse = 3x = 3 × 4 = 12 cm

★ We also know that ★

★ Area of triangle = 1 / 2 Base × height ★

Now, substitute the values :-

➹ Area of triangle = 1 / 2 16 × 12

➹ Area of triangle = 16 × 6

➹ Area of triangle = 96 cm²

Hence,

• The Area is 96 cm².