Question

The base and hypotenuse of a right triangle is 3cm and 13cm long. find its area
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Answer 1

Given :

• The base and hypotenuse of a right triangle is 5cm and 13cm.

To Find :

• Area of the right triangle.

Solution :

Suppose ABC be the triangle in which

1. BC = 5cm
2. AC = 13cm
3. AB = ?

We've to find perpendicular.

As we know that

• AC² = AB² + BC² [ Pythagoras theorem ]

Now

→ (13)² = AB² + (5)²

→ 169 = AB² + 25

→ AB ² = 169 - 25

→ AB² = 144

→ AB = √144

→ AB = 12cm

Perpendicular = 12cm

As we know that

Area of a right triangle = ½ × base × height

According to question :

→ Area = ½ × base × height

→ Area = ½ × 5 × 12

→ Area = 5 × 6

→ Area = 30cm²

Hence,

• Area of the right triangle = 30cm²

Answer 2

Correct Question

• The base and hypotenuse of a right triangle is 5cm and 13cm long. Find its area.

Given

• Base of the triangle = 5cm
• Hypotenuse of the triangle = 13cm

⠀

To find

• Area of the triangle.

⠀

Solution

• To calculate area of the triangle, we need to find the perpendicular.

⠀

$\: \: \: \: \sf\underline{Since,\: the\: given\: triangle\: is\: a} \\ \: \: \: \: \: \: \: \: \: \sf\underline{right\: angled\: triangle}$

⠀

• Using Pythagoras theorem

$\large{\boxed{\boxed{\sf{(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2}}}}$

⠀

$\tt\longrightarrow{(13)^2 = (5)^2 + (Perpendicular)^2}$

⠀

$\tt\longrightarrow{169 = 25 + (Perpendicular)^2}$

⠀

$\tt\longrightarrow{(Perpendicular)^2 = 169 - 25}$

⠀

$\tt\longrightarrow{(Perpendicular)^2 = 144}$

⠀

$\tt\longrightarrow{Perpendicular = \sqrt{144}}$

⠀

$\bf\longrightarrow{Perpendicular = 12}$

⠀

• Now, we have

⠀⠀⠀⠀⠀→ Base = 5cm

⠀⠀⠀⠀⠀→ Perpendicular/height = 12cm

⠀

We know that

$\large{\boxed{\boxed{\sf{Area_{(Triangle)} = \dfrac{1}{2} \times b \times h}}}}$

⠀

Here,

• b = base
• h = height

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = \dfrac{1}{\cancel{2}} \times 5 \times \cancel{12}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = 5 \times 6}$

⠀

$\bf:\implies\: \: \: \: \: \: \: \: {Area = 30}$

⠀

Hence,

• Area of the given triangle is 30 cm².

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