Question

each of equal sides of an isotope angle is 4 cm greater than its height if the base of the triangle is 24 cm calculate the perimeter and the area of the triangle​

Answer 1

Let the congruent side of the isosceles triangle be a and the height be h.

Given a=h+4

Since the height of the triangle, divides it into two right angled triangles,

a

2

=h

2

+(

2

b

)

2

=>(h+4)

2

=h

2

+12

2

h

2

+16+8h=h

2

+144

8h=128

h=16cm

a=20cm

Perimeter of the triangle = Sum of all sides =a+a+b=20+20+24=64cm

Area of triangle =

2

1

× base × height =

2

1

×24×16=192 sq cm

Answer 2

$\large \sf \underline{ \underline{Appropriate \: Question:- }}$

Each of equal sides of an isosceles triangle is 4 cm is greater than its height. If the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.

$\underbrace{ \underline{ \bf{Understanding \: the \: Concept:- }}}$

Here we are given that the sides of Isosceles triangle is greater than its height.And the base is 24 cm .Here we will apply pythagoras theorem We will first find the sides and then calculate the area and perimeter of triangle.

$\huge{ \sf { \underline{ \underline{ \color{maroon}{Solution:- }}}}}$

Let the height be x cm

$\boxed{ \underline{ \bf{ \green{Given \: that \: the \: equal \: sides \: are \: (x+4) cm}}}}$

$\bf \: Applying \: pythagoras \: theorem : -$

$➥ {(x + 4)}^{2} = {x}^{2} + {12}^{2}$

$➥8x = 128$

$➥x = \frac{128}{8}$

$➥x = 16 \: cm$

$\sf \: Area \: of \: Isosceles \: triangle \: is = \frac{1}{2} \times b \times h$

Given:-

A= x+4=16+4=20 cm

B= 24 cm ____(given)

$➥ \boxed{ \frac{1}{2} \times b \times \sqrt{ {4a}^{2} - {b}^{2} } }$

$➥ = \frac{1}{2} \times 24 \times 16 = 192 \: cm$

Area of triangle is 192 cm²

Perimeter of Isosceles triangle =2a+b

➥2×20 cm+24 cm

➥ 40 cm+ 24 cm

➥ 64 cm

━━━━━━━━━━━━━━━━━━━━━━━━

Formulas of perimeter:-

➥Perimeter of rectangle =2×(length +breadth)

➥Perimeter of square =4×side

➥Perimeter of triangle = sum of all sides

➥ Circumference of circle =2πr

╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾

Formulas of area:-

➥Area of rectangle= length ×breadth

➥Area of square =side²

➥Area of circle =πr²

➥Area of triangle = ½×base×height

╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾