Question

if the area of an isoscles right angled triangle is 72 square then it's perimeter is​

Answer 1

★Answer:–

The formula for finding the area of a right angle triangle is (a*b)/2=area.

Since this is an isosceles right triangle, side a=side b so we can rewrite the formula to (a*a)/2=72cm Multiply by 2

(a*a)=144 Remove parenthesis.

a^2=144 Take the square root of each side.

a=12 m for 2 sides of the triangle. The formula for the hypotenuse is a^2+b^2=c^2 or 12squared+12squared=c^2 or

144+144=c^2 or

c^2=288 Take the square root of both sides.

c=17cm The perimeter then is 12+12+17=41cm.

Answer 2

In isosceles right triangle base and perpendicular are of same length

i.e. b = p

Where, p is the height & b is the base of ∆.

Area of isosceles ∆ = 72 sq. units

→ 1/2 x base x height = 72

→ base x height = 144

→ b x p = 144

→ b² = 144

So, b = 12 = p

So,

h² = p² + b²

h² = 12² + 12²

h² = 288

hypotenuse, h = 17 (approx)

Hence,

Perimeter = p + b + h = 12 + 12 + 17 = 41 units

Hope it helps...

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