Question

the lengths of the sides of a triangle are in the extended ratio 7:8:9 the perimeter of the triangle is 96cm. what are the lengths of the sides?

Answer 1

Given :

• The length of the sides of the triangle are in the ratio 7:8:9 .
• The Perimeter of the Triangle is 96 cm.

To Find :

• The length of the sides of the triangle.

Solution :

Let us assume the sides be 7x cm, 8x cm and 9x cm.

We know,

`\qquad{ \bold{ \pmb{Sum \: of \: all \: sides \: of \: the \: triangle = Perimeter_((Triangle))}}}</p><p>`

So, Substituting the values :

`\qquad { \dashrightarrow{ \sf{7x + 8x + 9x = 96}}}`

`\qquad { \dashrightarrow{ \sf{24x= 96}}}`

`\qquad { \dashrightarrow{ \sf{ (24x)/(24) = (96)/(24) }}}`

`\qquad { \dashrightarrow{ \bf{ x = 4 }}}`

Therefore,

The length of the sides of the triangle are :

`\qquad { \dashrightarrow{ \sf{ 7x \: cm= 7 * 4 \: cm = \bf \: 28 \: cm }}}`

`\qquad { \dashrightarrow{ \sf{ 8x \: cm= 8 * 4 \: cm = \bf \: 32 \: cm }}}`

`\qquad { \dashrightarrow{ \sf{ 9x \: cm= 9 * 4 \: cm = \bf \: 36 \: cm }}}`

Answer 2

28 cm, 32cm , 36cm

Explanation:

Given:

• The lengths of the sides of a triangle are in the ratio 7:8:9
• Perimeter of triangle is 96cm

To Find:

• The lengths of the sides of triangle?

Solution:

Let:

• 1st side = 7x
• 2nd side = 8x
• 3rd side = 9x

As, we know that,

★ Perimeter of Triangle = Sum of all sides ★

➝ 7x + 8x + 9x = 96cm

➝ 24x = 96cm

➮ x = 96/24

➮ x = 4

So, length of the sides are:

7x = 7 × 4 ➝ 28cm

8x = 8 × 4 ➝ 32cm

9x = 9 × 4 ➝ 36cm