Question

Find the area of the right-angled triangle with hypotenuse 40cm and one of the other two sides 24cm

Answer 1

Answer:

$\boxed{Text}$ Answer:By Pythagoras theorem we have:a^2+b^2=c^2,24^2+x^2 =40^2,576+x^2=1600,x^2=1600-576,x^2=1024,√x^2=√1024,x=32,area of a right angled triangle=1÷2×product of its legs,area=1/2(24×32)cm2,=(1/2×768cm2),=384cm2

Answer 2

GiveN :-

• Hypotenuse of the triangle = 40 cm

• Base of the triangle = 24 cm

To FinD :-

• Area of the triangle

SolutioN :-

Firstly we have to find perpendicular ( height ) of the triangle by using Pythagoras theorem

$\longrightarrow \boxed{ \sf{H}^{2} ={B}^{2} +{P}^{2} }\\ \\\longrightarrow \sf {(40)}^{2} = {(24)}^{2} ={P}^{2} \\ \\ \longrightarrow \sf1600 = 576 = {P}^{2} \\ \\\longrightarrow \sf {P}^{2} =1600 - 576 \\ \\\longrightarrow \sf P = \sqrt{1024} \\ \\\longrightarrow \sf P = 32 \: cm$

Height of the triangle is 32 cm

Now , Area of the triangle is :

$\longrightarrow \boxed { \blue{ \sf Area = \frac{1}{2} \times base \times height} }\\ \\\longrightarrow \sf Area = \frac{1}{2} \times 24 \times 32 \\ \\\longrightarrow \sf Area =12 \times 32 \\ \\ \longrightarrow \boxed{\sf Area =384 \: {cm}^{2}}$

$\large \therefore \: \underline{ \green{\bf Area \: of \: the \: triangle \: is \: 384 \: {cm}^{2} }}$