Question

In triangle abc the length of bc is less than twice the length of ab by 3cm. The length of ac exeeds the length of ab by 9cm. The perimeter of triangle is 34cm.find smallest side

Answer 1

Answer

The smallest side is AB and is 7cm

$\bf\large\underline{Given}$

• In ∆ABC , the length of BC is less than twice the length of AB by 3cm
• The length of AC exceeds the length of AB by 9cm
• The perimeter of the triangle is 34cm

$\bf\large\underline{To \ Find}$

• The smallest side

$\bf\large\underline{Solution}$

Let us consider the sides AB , BC and AC be x cm, y cm and z cm

We are given that ,

$\sf\implies 2x = y + 3cm \\\\ \sf\implies y = 2x - 3cm \dashrightarrow (1)$

And

$\sf\implies z = x + 9cm \dashrightarrow (2)$

Again, by question

$\sf perimeter \: of \: the \: triangle = 34 \\ \\ \sf \implies x + y + z = 34 \\ \\ \sf \implies x + 2x - 3 + x + 9 = 34 \\ \\ \sf \implies 4x + 6 = 34 \\ \\ \sf \implies 4x = 28 \\ \\ \sf \implies x = 7$

Therefore , the side AB is 7cm

Now we have from (1) and (2)

$\sf y = 2 \times 7 - 3 \: \: and \: \: \: z =7 + 9 \\ \\ \sf \implies y = 11 \: \: and \: \: \implies z = 16$

Thus , the other sides of the triangle BC and AC are 11cm and 16cm

Hence , the smallest side is AB of 7cm