An isoceles right triangle has an area of 8 cm 2- Find the length of its hypotenuse

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

An isoceles r...

Question

An isoceles right triangle has an area of 8 cm². Find the length of its hypotenuse

Open in App

Solution

Both the perpendicular and base are equal in length.

So Area of triangle = 1/2 x b x h

Let b = h = y

1/2 x y x y = 8
y² = 16
y = 4

So Perpendicular = Base = 4 cm

Now by Pythagoras theorem,
4² + 4² = √ 16+ 16 = √32 = 4√2 cm

So required hypotenuse = 4√2 cm

Suggest Corrections

Similar questions

Q. Question 1
An isosceles right triangle has area

8 c m^{2}

. The length of its hypotenuse is

Q. An isosceles right angled triangle has area

8 c m^{2}

. Find the length of its hypotenuse.

Q. Question 1
An isosceles right triangle has area

8 c m^{2}

. The length of its hypotenuse is

If an isosceles right triangle has area $8 c m^{2}$ then the length of its hypotenuse is
(a) $\sqrt{32} c m$
(b) $\sqrt{48} c m$
(c) $\sqrt{24} c m$
(d) $\sqrt{4} c m$

Q. An isosceles right-angled triangle has area

200 c m^{2}

What is the length of its hypotenuse

?

Join BYJU'S Learning Program

An isoceles right triangle has an area of 8 cm2​​​​​​. Find the length of its hypotenuse

Both the perpendicular and base are equal in length. So Area of triangle = 1/2 x b x h Let b = h = y 1/2 x y x y = 8 y² = 16 y = 4 So Perpendicular = Base = 4 cm Now by Pythagoras theorem, 4² + 4² = √ 16+ 16 = √32 = 4√2 cm So required hypotenuse = 4√2 cm

An isoceles right triangle has an area of 8 cm². Find the length of its hypotenuse

Both the perpendicular and base are equal in length.

So Area of triangle = 1/2 x b x h

Let b = h = y

1/2 x y x y = 8
y² = 16
y = 4

So Perpendicular = Base = 4 cm

Now by Pythagoras theorem,
4² + 4² = √ 16+ 16 = √32 = 4√2 cm

So required hypotenuse = 4√2 cm