Question

The Perimeter of an Isosceles triangle is 42 cm. The ratio of the equal side to its base is 3: 4. Find the area of the triangle.

Answer 1

GIVEN :-

Perimeter = 42 cm

Ratio of 2 equal side and base = 3 : 4

TO FIND :-

Area of Triangle

SOLUTION :-

Equal side = $\sf 3x$

$\therefore$ Two Equal side = $\sf 3x+3x$

Base = $\sf 4x$

So, Perimeter = side + side + side

$\sf 42$ = $\sf 3x+3x+4x$

$\sf 42$ = $\sf 10x$

$\sf x$ = $\sf \frac{42}{10}$

$\sf\fbox{x = 4.2}$

Measure of sides :-

• Side = $\sf \fbox\green{3x = 3×4.2=12.6\: cm}$
• Side = $\sf \fbox\green{3x = 3×4.2=12.6\: cm}$
• Base = $\sf \fbox\green{4x = 4×4.2=16.8\: cm}$

We know that,

Heron's formula :

$\sf {\sqrt{s(s - a)(s - b)(s - c)}}$

Here,

s = Semi Perimeter

a, b, c = sides

☞ So, Semi Perimeter = $\sf \frac{Perimeter}{2}$

→ Semi Perimeter = $\sf \frac{42}{2}$

→ Semi Perimeter = $\sf 21$

⇒ Semi Perimeter is 21 cm.

Now,

→ Area = $\sf {\sqrt{21(21 - 12.6)(21 - 12.6)(21 - 16.8)}}$

→ Area = $\sf {\sqrt{21×8.4×8.4×4.2}}$

→ Area = $\sf {8.4×\sqrt{88.2}}$

→ Area = $\sf {8.4×9.392}$

→ Area ≈ $\sf {78.893}$

∴ Area of Triangle is 78.893 cm².

Answer 2

Answer:

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Step-by-step explanation:

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