Question

The sides of a triangle are 6:8:10. If the perimeter of the triangle is 288cm,find the
i. longest side
ii. shortest side
iii. difference between the longest side and shortest side.

Answer 1

${\mathfrak{\underline{ Given : }}}$

• The sides of a triangle are 6:8:10.

• And the perimeter of the triangle is 288cm.

${\mathfrak{\underline{ To \: \: find : }}}$

1. Longest side.
2. Shortest side.
3. And the difference between both.

${\mathfrak{\underline{ Solution : }}}$

Let's assume that :

Sides of the ∆ are :- 6x(shortest side), 8x, and 10x(longest side)

We know that,

$\gray \dag{ \underline{ \boxed{ \mathfrak{perimeter \: of \: a \: \triangle \: = \sf{ a + b + c}}}}} \gray \dag$

Where,

➠ a + b + c (represents) → 6x + 8x + 10x.

➠ Perimeter of the ∆ → 288cm (given).

$☯ \begin{gathered}\underline{\boldsymbol{According\: to \:the\: question :}}\\\end{gathered}$

${ \gray { \rm \leadsto \: perimeter \: of \: the \: \triangle \to \: a + b + c }}$

$\rm \leadsto \: 288 = 6x + 8x + 10x$

$\rm \leadsto \: 288 = 24x$

$\rm \leadsto \: x = { \cancel{\frac{288}{24}}}$

$\bf \therefore \: x = 12cm.$

After solving we get :

x = 12cm.

Hence,

The other sides :

➠ 6x = 6 × 12 = 72cm.

➠ 8x = 8 × 12 = 96cm.

➠ 10x = 10 × 12 = 120cm.

${\mathfrak{\underline{ Required \: Answer : }}}$

(i) Shortest side → 72cm.

(ii) Longest side → 120cm.

(iii) Difference between them :

→ (120 - 72)cm.

→ 48cm.

Hence, we are done.