Question

The area of a right angled triangle whose base is 8cm and its hypotenuse is 17cm is ___________cm2

Answer 1

Given :

• base of right angled triangle = 8 cm

• hypotenuse = 17cm

To find :

• Area of triangle

Formula used :

$p = \sqrt{ {h}^{2} - {b}^{2} }$

$A = \dfrac{1}{2} \times b \times p$

Where :-

• p = perpendicular or height

• h = hypotenuse

• b = base

• A = area of triangle

Solution :

To find area of triangle first we will find height of the triangle :-

$\implies \: p = \sqrt{ {h}^{2} - {b}^{2} }$

put :-

• h = 17
• b = 8

$\implies \: p = \sqrt{ {(17)}^{2} - {(8)}^{2} }$

$\implies \: p = \sqrt{ 289 - 64}$

$\implies \: p = \sqrt{ 225}$

$\implies \: p = \sqrt{ 15 \times 15}$

$\implies \: p = 15 \: cm$

therefore the value of perpendicular or height = 15 cm.

Now we will find area of triangle :-

$\implies \: A = \dfrac{1}{2} \times b \times p$

put :-

• b = 8
• p = 15

$\implies \: A = \dfrac{1}{2} \times 8\times 15$

$\implies \: A = \dfrac{1}{1} \times 4\times 15$

$\implies \: A = 4\times 15$

$\implies \: A = 60 \: {cm}^{2}$

therefore area of triangle = 60 cm²

Answer :

The area of a right angled triangle whose base is 8cm and its hypotenuse is 17cm is 60 cm².

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$\large\bf\red{Additional-Information}$

Area of circle = πr²

Circumference of circle = 2πr

Area of square = (side)²

perimeter of square = 4× side

area of Rhombus = 1/2(diagonal 1)(diagonal 2)

Area of rectangle = length × breadth

Perimeter of rectangle = 2( length + breadth)

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Answer 2

Given ,

• Base of triangle (B) = 8 cm
• Hypotenuse (H) = 17 cm

We know that , in right angled triangle

(H)² = (B)² + (P)²

Thus ,

(17)² = (8)² + (P)²

289 = 64 + (P)²

(P)² = 225

P = ±√225

P = ± 15 cm

Since , the length can't be negative

Therefore , the height of triangle is 15 cm

Now , the area of triangle is given by

$\boxed{ \tt{Area \: of \: triangle = \frac{1}{2} \times base \times height}}$

Thus ,

Area = 1/2 × 8 × 15

Area = 4 × 15

Area = 60 cm²

Therefore , the area of triangle is 60 cm²

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