Question

The base of a right triangle is 8 cm and hypotenuse is 10 cm.Its area will be

Answer 1

Answer:

Area of right triangle = 24 $cm^{2}$

Step-by-step explanation:

Given that:-

Base of right angle = 8 cm

Hypotenuse of right angle = 10 cm

By pythagoras theorem:-

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

$10^{2} = 8^{2} + h^{2}$

$100 = 64 + h^{2}$

$100 - 64 = h^{2}$

$h^{2} = 36$

Height = 6 cm

Area of right triangle = $\dfrac{1}{2}[Base\times Height]$

                                   = $\dfrac{1}{2}[8 \times 6]$

                                   = $\dfrac{48}{2}$

Area of right triangle = 24 $cm^{2}$

Answer 2

$\bf{\huge{\underline{\boxed{\sf{\green{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\red{Given:}}}}}$

• Base of a right triangle is 8 cm
• Hypotenuse is 10 cm

$\bf{\underline{\underline{\sf{\red{To\:find:}}}}}$

• Area of the triangle

$\bf{\underline{\underline{\sf{\red{Solution:}}}}}$

Let base of the triangle be x cm = 8 cm

Let height of the triangle be y cm.

Hypotenuse = H = 10 cm

Since the triangle is right angled triangle.

$\bf{\underline{\underline{\sf{\purple{By\:Pythagoras\:Theorem:}}}}}$

=> Hypotenuse² = x² + y²

=> 10² = 8² + y²

=> 100 = 64 + y²

=> 100 - 64 = y²

=> 36 = y²

=> $\sqrt{36}$ = y

=> 6 = y

Height = y = 6 cm

Now using the formula for area of the triangle we can calculate the area.

$\bf{\large{\underline{\boxed{\sf{\pink{Area\:of\:triangle\:=\:\frac{1}{2}\:\times\:base\:\times\:height}}}}}}$

Plug in the values,

=> Area = ½ × 8 × 6

=> Area = 4 × 6

=> Area = 24 sq.cm

Area of triangle = 24 cm²

$\bf{\huge{\underline{\boxed{\sf{\green{Verification:}}}}}}$

For hypotenuse :-

Hypotenuse = 10 cm

Base = x = 8 cm

Height = y = 6 cm

=>Hypotenuse² = x² + y²

=> 10² = 8² + 6²

=> 100 = 64 + 36

=> 100 = 100

LHS = RHS.

For area of triangle :-

Plug in the values of base and area of the triangle in the formula for "area of a triangle."

=> Area = ½ × x × y

=> 24 = ½ × 8 × y

=> 24 = ½ × 8y

=> 24 × 2 = 8y

=> 48 = 8y

=> $\large\frac{48}{8}$ = y

=> 6 = y

y = 6

•°• Our answer is right.