Question

perimeter of an isosceles triangle is 150m if its unequal side is 70m find the area of the triangle​

Answer 1

Attachment :- Fig. of the question

$\mathtt{\huge{\bf{\underline{\red{Given :-}}}}}$

• The perimeter of an isosceles triangle is 150m.

• The unequal side of triangle is 70 m.

$\mathtt{\huge{\bf{\underline{\blue{To\:Find:-}}}}}$

• The area of the triangle .

$\mathtt{\huge{\bf{\underline{\green{Solution:-}}}}}$

We know, that iscoscales triangle is a triangle having two sides equal & one unequal .

According to the question,

• The perimeter of an isosceles triangle = 150m...(1)

• The perimeter of an isosceles triangle =

2a+b..(2)

From equation 1 & 2 ,

2 a + b = 150

• One of our unequal side is 70m.

So, b is our unequal side.

➝ 2 a + 70 = 150

➝ 2 a = 150 - 70

➝ 2 a = 80

➝ a = $\dfrac{80}{2}$

➝ a = $\cancel{\dfrac{80}{2}}$

➝ a = 40 m

We got, The two equal sides of triangle = 40 cm.

★ Area of Isoscales Triangle = ${\dfrac{1}{2}$ × b × h

b = base = 40 m

h = hieght of triangle or ⟂ side = 40 m

So , using given in formulae

Area of Isoscales Triangle = ${\dfrac{1}{2}$ × b × h

➝ $\dfrac{1}{2}$ × 40 × 40

➝ $\dfrac{1600}{2}$

➝ $\cancel{\dfrac{1600}{2}}$

➝800 m²

Hence, The area of the triangle is 800 m² .

________________________________________

Answer 2

Given :-

Perimeter of an isosceles triangle = 150 m

Measure of the unequal side = 70 m

To Find :-

The area of the triangle.

Solution :-

We know that,

• p = Perimeter
• s = Semi perimeter
• a = Area

According to the question,

Perimeter of triangle = Sum of all sides

Let the two equal sides be 'x'.

Making an equation,

70 + x + x = 150

70 + 2x = 150

By transposing,

2x = 150 - 70

2x = 80

Finding x,

x = 80/2

x = 40 m

Therefore, the other two sides of the isosceles triangle is 40 m each.

Finding semi perimeter,

$\underline{\boxed{\sf Semi \ perimeter=\dfrac{a+b+c}{2} }}$

Given that,

Unequal side = 70 m

Two equal side = 40 cm each

Perimeter (p) = 150 m

Substituting their values,

40+40+70/2 = 150/2

= 75 m

Using Heron's formula,

$\underline{\boxed{\sf Area \ of \ triangle=\sqrt{s(s-a)(s-b)(s-c)} }}$

Given that,

Unequal side = 70 m

Two equal side = 40 m each

Semi perimeter (p) = 75 m

Substituting their values,

$\sf =\sqrt{75(75-40)(75-40)(75-70)}$

$\sf =\sqrt{75 \times 35 \times 35 \times 5}$

$\sf =35\sqrt{5 \times 5 \times 3 \times 5}$

$\sf =35 \times 5 \times \sqrt{15}$

$\sf =175 \times 3.87$

$\sf =677.25 \ m^2$

Therefore, the area of the triangle is 677.25 m².