Question

The three sides of a triangle are n, 4n+4, and 5n−13. If the perimeter of the triangle is 91cm, what is the length of each side?

Answer 1

Given :

Perimeter of the triangle = 91 cm.

Sides of the triangle = n,4n+4,5n-13

To Find :

The length of each side.

Solution :

We know very well that the perimeter of a triangle is given by the formulae :

Sum of all the sides of the triangle.

Then ,

n+4n+4+5n-13 = 91

10n -9 = 91

10 n = 91+9

10 n = 100

n = 10 cm

Then the sides are :

n,4n+4,5n-13

= 10cm , 44 cm , 37 cm

Answer 2

HELLO DEAR FRIEND

YOUR ANSWER

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$\large \bf \boxed{ \boxed{10 \: cm} \: \: \boxed{44 \: cm} \: \: \boxed{47cm}}$

$\huge \bf \underline \red{ \mathbb {STEP \: \: BY \: \: STEP}}$

$\huge\bf \underline \red{ \mathbb {EXPLANATION }}$

GIVEN SIDES OF TRIANGLE = n, 4n+4, and 5n−13.

PERIMETER = SUM OF ALL SIDES

GIVEN PERIMETER = 91 CM

ATQ,

n + 4n+4 + 5n−13 = 91

10n - 9 = 91

10n = 91 + 9

10n = 100

$\large{ \frac{ \large{100}}{ \large{10}} }$

$\huge{= } \: \: \large { \boxed{ \bf{ 10} \: cm}}$

NOW GIVEN SIDES =

n =

$\: \: \large { \boxed{ \bf{ 10 \: cm}}}$

4n + 4

= 4(10) + 4

= 40 + 4

$\huge{= } \: \: \large { \boxed{ \bf{ 44 } \: cm}}$

5n - 13

= 5(10) - 13

= 50 - 13

$\huge{= } \: \: \large { \boxed{ \bf{ 37 } \: cm}}$

SO,

THE SIDES OF THE TRIANGLE ARE

⏬⏬⏬⏬⏬⏬

$\large \bf \boxed{ \boxed{10 \: cm} \: \: \boxed{44 \: cm} \: \: \boxed{37cm}}$

HOPE IT HELPS

THANKS