# The Lengths of the Sides of a Triangle Are in the Ratio 3 : 4 : 5 and Its Perimeter is 144 Cm. Find the Area of the Triangle and the Height Corresponding to the Longest Side. - Mathematics

The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.

#### Solution

Let the sides of a triangle are 3x, 4x and 5x.
Now, a = 3x, b = 4x and c = 5x
The perimeter 2s = 144
⇒ 3x + 4x + 5x = 144 [∵ a + b + c = 2s]
⇒ 12x = 144
⇒ x = 12
∴ sides of triangle are a = 3(x) = 36cm
b = 4(x) = 48 cm
c = 5(x) = 60 cm

Now semi perimeter s1/2(a+b+c)=1/2(144)=72cm

By heron’s formulas ∴ Area of Δle = sqrt(s(s-a)(s-b)(s-c))

=sqrt(72(72-36)(72-48)(72-60)

=864cm^2

Let l be the altitude corresponding to longest side,∴1/2xx60xxl=864

⇒l=(864xx2)/60

⇒l=28.8cm

Hence the altitude one corresponding long side = 28.8 cm

Concept: Area of a Triangle by Heron's Formula
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.1 | Q 9 | Page 8