Question

The base of a right triangle is 10 cm and hypotenuse i's 26 cm, Find the area of triangle.

Answer 1

Answer:

Therefore, area of triangle will be 120 sq.cm

Answer 2

Answer :-

• The area of the triangle = 120 cm².

To find :-

• The area of the triangle.

Step-by-step explanation :-

• Before finding the area of the triangle, let's find it's perpendicular!

We know that :-

$\bigstar \: \underline{\boxed{\sf Hypotenuse^2 = Base^2 + Perpendicular^2}}$

Here :-

• Base = 10 cm.
• Hypotenuse = 26 cm.

Let :-

• The perpendicular of the triangle be "P".

Substituting the given values in this formula -

$\longrightarrow \tt H^2 = B^2 + P^2$

$\longrightarrow \tt 26^2 = 10^2 + P^2$

$\longrightarrow \tt 676 = 100 + P^2$

$\longrightarrow \tt 676 - 100 = P^2$

$\longrightarrow \tt 576 = P^2$

$\longrightarrow \tt \sqrt{576} = P$

$\longrightarrow \tt 24 \: cm = P$

________________________________

• Now, let's find the area of the triangle!

We know that -

$\bigstar \: \underline{\boxed{\sf Area_{(triangle)} = \dfrac{1}{2} \times Base \times Height}}$

Here -

• Base = 10 cm.
• Height = 24 cm.

Therefore -

$\mapsto \rm Area_{(triangle)} = \dfrac{1}{2} \times 10 \times 24$

$\rm\mapsto Area_{(triangle)} = \dfrac{1}{2} \times 240$

$\rm\mapsto Area_{(triangle)} = \cancel{\dfrac{240}{2} }$

$\rm \mapsto Area_{(triangle)} = 120 \: {cm}^{2}$

Hence -

• The area of the triangle is 120 cm².

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