Question

The perimeter of a triangle is 84cm and it's area is 336cm². If one of it's sides is 30cm, find the length of other two sides. ​

Answer 1

The other side lengths of the triangle are 26 and 28 cm

How to determine the other lengths?

The perimeter (P) is given as:

P = 84 cm

The area is given as:

A = 336

Let the sides be x, y and z.

So, we have:

x + y + z = 84

By herons' formula, we have:

$Area = \sqrt{s(s-x)(s-y)(s-z)}$

Where:

s = 0.5(x + y + z)

Multiply by 2

2s = x + y + z

Recall that:

x + y + z = 84

So, we have:

2s = 84

Divide by 2

s = 42

Let x = 30 ---- the given side length

So, we have:

30 + y + z = 84

Subtract 30 from both sides

y + z = 54

Make y the subject

y = 54 - z

Recall that

$Area = \sqrt{s(s-x)(s-y)(s-z)}$

The area is 336. So, we have:

$336 = \sqrt{s(s-x)(s-y)(s-z)}$

Square both sides

112896 = s(s-x)(s-y)(s-z)

Substitute values for x, y and s

112896 = 42(42-30)(42 - (54 - z))(42 - z)

Divide through by 42

2688 = (42-30)(42 - (54 - z))(42 - z)

Divide through by 12

224 = (42 - (54 - z))(42 - z)

Evaluate the brackets

224 = (z - 12)(42 - z)

Using a graphing calculator, we have:

z =26 or z = 28

Recall that:

y = 54 - z

So, we have

y = 54 - 26 = 28

y = 54 - 28 = 26

Hence, the other side lengths of the triangle are 26 and 28 cm

Read more about triangles at:

brainly.com/question/1675117

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