Question

in a right angle triangle the side forming the right angle measure 15 cm and 20 cm. find its area, hypotenuse, perimeter and, the length of perpendicular from the vertex of the right angle to the hypotenuse?
$please \: answer \: me \: fast \:$
​

Answer 1

Step-by-step explanation:

hope it'll help you........

Answer 2

$\rule{205}3$

Given :-

↪ The sides forming the right angle in the right angled triangle are 15 cm and 20 cm

To find :-

• area of triangle
• hypotenuse of triangle
• perimeter of triangle
• length o perpendicular from right angle vertex on hypotenuse

Knowledge required :-

$\boxed{\begin{minipage}{7.5cm}\implies\sf{ area\; of \;triangle=\frac{1}{2}\times base\times height}\\\\\implies\sf{Pythagoras\: theorem}\\\sf{(hypotenuse)^2=(height)^2+(base)^2}\\\\\implies\sf{perimeter\; of\; triangle=sum \;of \;all \;sides}\\\\\implies\sf{Theorem: when\; perpendicular\; is\;drawn\;from\; }\\\sf{the\;right\;angle\;vertex\;then\;the\;triangles\;on\;the \;both}\\\sf{sides\;of\;perpendicular\;are\;similar\;to\;each\;other\;and}\\\sf{similar\;to\;the\;main\;triangle.}\end{minipage}}$

Solution :-

Refer to the figure attached

Finding the area of triangle

area of triangle = $\sf{\frac{1}{2}\times base \times height}$

area of triangle = $\sf{\frac{1}{2}\times 20 \times 15 =150\;cm^2}$

Finding the hypotenuse of triangle

Using Pythagoras theorem

(hypotenuse)² = (base)² + (height)²

(hypotenuse)² = ( 20 )² + ( 15 )²

hypotenuse = 25 cm

Finding the perimeter of triangle

perimeter of triangle = 20 + 15 + 25 cm

perimeter of triangle = 60 cm

Finding the length of perpendicular from right angle vertex

Consider the figure

Using the theorem mentioned in knowledge required

Δ ABD ~ Δ ACB

so,

$\sf{\frac{AB}{BD}=\frac{AC}{BC}}$

putting known values

$\sf{\frac{15}{BD}=\frac{25}{20}}$

BD = 12 cm

$\rule{205}3$