Question

The lengths of the sides of a triangle are in the extended ratio 5: 8:10. The perimeter of the triangle is 115 cm. What are the lengths of the sides?
The lengths of the sides in cm are ____

Answer 1

Given :

• The length of the sides of the triangle are in the ratio 5:8:10 .
• The Perimeter of the Triangle is 115 cm.

To Find :

• The length of the sides of the triangle.

Solution :

Let us assume the sides be 5x cm, 8x cm and 10x cm.

We know,

$\qquad{ \bold{ \pmb{Sum \: of \: all \: sides \: of \: the \: triangle = Perimeter_{(Triangle)}}}}$

So, Substituting the values :

$\qquad { \dashrightarrow{ \sf{5x + 8x + 10x = 115}}}$

$\qquad { \dashrightarrow{ \sf{23x= 115}}}$

$\qquad { \dashrightarrow{ \sf{ \dfrac{23x}{23} = \dfrac{115}{23} }}}$

$\qquad { \dashrightarrow{ \bf{ x = 5 }}}$

Therefore,

The length of the sides of the triangle are :

$\qquad { \dashrightarrow{ \sf{ 5x \: cm= 5 \times 5 \: cm = \bf \: 25\: cm }}}$

$\qquad { \dashrightarrow{ \sf{ 8x \: cm= 8 \times 5 \: cm = \bf \: 40 \: cm }}}$

$\qquad { \dashrightarrow{ \sf{ 10x \: cm= 10 \times 5 \: cm = \bf \: 50 \: cm }}}$