Question

An isosceles right triangle has area 18 cm2

. The length of its hypotenuse is ______.​

Answer 1

Answer:

The length of the hypotenuse angle is √72 cm

Step-by-step explanation:

Given: An isosceles right triangle has an area  18 $cm^{2}$

To find: The length of its hypotenuse triangle

Solution:

Let us consider height of the triangle = h

We know that,

base of the triangle= height of the triangle = h

According to the given statement,

Area of the triangle = 18 $cm^{2}$

We know that

Area of the triangle = $\frac{1}{2} bh$

⇒ 18 = $\frac{1}{2}$ × h × h

⇒ 18 = $\frac{1}{2} h^{2}$

⇒ 36 = $h^{2}$

⇒ h = 6

h = 6 cm

We know that base = height

Base = height = 6

$(Hypotenuse)^{2} = (Base)^{2} + (Height)^{2}$

⇒  $(Hypotenuse)^{2} = (6)^{2} + (6)^{2}$

⇒  $(Hypotenuse)^{2} = 36+36$

⇒  $(Hypotenuse)^{2} = 72$

Hypotenuse = √72

Final answer:

The length of the hypotenuse is √72 cm

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Answer 2

Answer:

Concept:

         A right triangle with two equal-length legs is called an isosceles right triangle. The corresponding angles would also be congruent because the lengths of the two legs of the right triangle are equal. As a result, the two acute angles and two legs of an isosceles right triangle are congruent.

Step-by-step explanation:

Given:

Area of an isosceles right triangle = 18 cm²

To find:

We have to find the length of its hypotenuse.

Solution:

We take, height of the triangle = h

In isosceles right triangle base 'b' is equal to height.

so we can write, base = h

Area of triangle = 18cm²

⇒ $\frac{1}{2}$ × b × h = 18

⇒ $\frac{1}{2}$ × h × h =18

⇒ $\frac{1}{2}$ × h² =18

h² = 18 × 2

h² = 36

h =√36

h = 6 cm

∴ base = height = 6cm

Hence the triangle is right angled,

Hypotenuse ² = Base²+ Height²

                       = 6² + 6²

                       = 36 + 36

Hypotenuse²    = 72

Hypotenuse = √72

Therefore the length of its hypotenuse is √72.

#SPJ3