Question

The perimeter of the right angled isosceles triangle is (8+4√2) cm, then area of the triangle is​

Answer 1

Answer:

area of triangle=8 cm square...

Answer 2

Area of the ∆ABC is 8 sq cm.

Given :

The perimeter of the right angled isosceles triangle is (8+4√2) cm.

To find out :

Area of the given triangle .

Solution :

ABC is a right angled triangle. A right angled triangle is a triangle in which one angle is a right angle or 90° .

An isosceles triangle is a triangle in which two sides of a triangle are congruent.

so let AB = BC = x cm

We know that

Perimeter of a triangle = Sum of all three sides of a triangle.

Perimeter of ∆ ABC = AB + BC + AC

We are given perimeter of ∆ ABC = 4√2

Hence

x + x + √x² + x²=

x + x + √2x² = 4√2

2x + √2x² = 4√2

2x + x√2 = 4√2

If we compare both the sides we get

2x + x = 8 +4

3x =12

x =4

so we got

AB = 4 cm

BC = 4 cm

now we have to find area of ∆ ABC .

we know formula for area of a triangle

Area of a triangle = 1/2 x base x height

= 1/2 x 4 x 4 sq cm

= 2x 4

= 8 sq cm

Hence area of ∆ ABC = 8 sq cm

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