In an isosceles right-angled triangle, the perimeter is 30 m. Find its

1.	In an isosceles right-angled triangle, the perimeter is 30 m. Find its area (Approximate)1. 38.63 m22. 40 m23. 39.60 m24. 37.86 m2
Answer» Correct Answer - Option 1 : 38.63 m² Given: Perimeter = 30 m Concept used: Perimeter of an isosceles triangle = 2x + y Area of an isosceles right angle triangle = 1/2 × x² x = equal sides of an isosceles triangle Calculation: In an isosceles right angled triangle, the two sides on the right angle are equal Let the equal sides be a Hence, hypotenuse of the isosceles right angled triangle = \(√ {{{\rm{a}}^2} + {{\rm{a}}^2}} = √ 2 {\rm{a}}\) \(\rm a + a\;+ √2a = 30\) ⇒ \(\rm 2a\;+ √2a = 30\) ⇒ \(\rm a(2\;+ √2) = 30\) ⇒ \(\rm a = \frac{30}{(2\;+ √2)}\) ⇒ \(\rm a = \frac{30(2\;-\; √2)}{(2\;+\;√2)(2\;-\; √2)}\) ⇒ \(\rm a = \frac{30(2\;-\; √2)}{2^2\;-\;(√2)^2}\) ⇒ \(\rm a = \frac{30(2\;-\; √2)}{4\;-\;2}\) ⇒ \(\rm a = \frac{30(2\;-\; √2)}{2}\) ⇒ \(\rm a = 15(2\;-\; √2)\) 1/2 × (15(2 – √2))² ⇒ 1/2 × 225(4 + 2 – 4√2) ⇒ 112.5(6 – 5.6568) [√2 = 1.4142] ⇒ 112.5(0.3432) ⇒ 38.626 ≈ 38.63 m ∴ Area of the triangle is 38.63 m (Approximate)

In an isosceles right-angled triangle, the perimeter is 30 m. Find its area (Approximate)1. 38.63 m22. 40 m23. 39.60 m24. 37.86 m2

Answer» Correct Answer - Option 1 : 38.63 m²

Given:

Perimeter = 30 m

Concept used:

Perimeter of an isosceles triangle = 2x + y

Area of an isosceles right angle triangle = 1/2 × x²

x = equal sides of an isosceles triangle

Calculation:

In an isosceles right angled triangle, the two sides on the right angle are equal

Let the equal sides be a

Hence, hypotenuse of the isosceles right angled triangle = \(√ {{{\rm{a}}^2} + {{\rm{a}}^2}} = √ 2 {\rm{a}}\)

\(\rm a + a\;+ √2a = 30\)

⇒ \(\rm 2a\;+ √2a = 30\)

⇒ \(\rm a(2\;+ √2) = 30\)

⇒ \(\rm a = \frac{30}{(2\;+ √2)}\)

⇒ \(\rm a = \frac{30(2\;-\; √2)}{(2\;+\;√2)(2\;-\; √2)}\)

⇒ \(\rm a = \frac{30(2\;-\; √2)}{2^2\;-\;(√2)^2}\)

⇒ \(\rm a = \frac{30(2\;-\; √2)}{4\;-\;2}\)

⇒ \(\rm a = \frac{30(2\;-\; √2)}{2}\)

⇒ \(\rm a = 15(2\;-\; √2)\)

1/2 × (15(2 – √2))²

⇒ 1/2 × 225(4 + 2 – 4√2)

⇒ 112.5(6 – 5.6568) [√2 = 1.4142]

⇒ 112.5(0.3432)

⇒ 38.626 ≈ 38.63 m

∴ Area of the triangle is 38.63 m (Approximate)