Question

The perpendicular sides of a right triangle are in the ratio 7:24 and its hypotenuse is 50 cm long. Find the perimeter and the area of the triangle. [Hint: Use Pythagorean Theorem]

Answer 1

Hi

Draw a rough diagram of a

right Triangle .

A
|
|7x
|
|__________________C
B. 24x

Join AC ,


It is given that ,

Ratio of perpendicular sides = 7:24

AB : BC = 7 : 24

Let AB = 7x cm

BC = 24x cm

AC = 50 cm

By Pythagorean theorem,

AB² + BC² = AC²

( 7x )² + ( 24x )² = ( 50 )²

49x² + 576x² = ( 50 )²

625x² = ( 50 )²

( 25x )² = 50²

25x = 50

x = 50/25

x = 2

Therefore ,

AB = 7x = 7 × 2 = 14 cm

BC = 24x = 24 × 2 = 48 cm

Now ,

Permeter of ∆ABC = AB + BC + CA

P = 14 + 48 + 50

P = 112 cm

Area of ∆ABC = ( AB × BC )/2

= ( 14 × 48 )/2

= 7 × 48

= 336 sq cm

I hope this helps you.

: )

Answer 2

Heya !!!

Let ∆ABC is an right triangle right angled at B.

In which,

AB : BC = 7:24

And,

Hypotenuse = 50 cm

Let X be common multiple to the ratio.

Then ,

AB = 7X and BC = 24X.

By pythagoras theroem,

(AC)² = (BC)² + (AB)²

(50)² = (24X)² + (7X)²

2500 = 576X² + 49X²

625X² = 2500

X² = 2500/625

X² = 4

X = ✓4 = 2 cm

BC = 24X => 24 × 2 = 48 cm

AB = 7X => 7 × 2 = 14 cm

Therefore,

Perimeter of triangle ABC = AB + BC + AC

=> 14 + 48 + 50

=> 112 cm

and,

Area of triangle ABC = 1/2 × Perpendicular × Base

=> 1/2 × AB × BC

=> 1/2 × 14 × 48



=> 7 × 48


=> 336 cm².



HOPE IT WILL HELP YOU...... :-)