Question

Two Sides Of A Triangle Are Each 5 Meters Less Than Twice The Third Side. If The Perimeter Of Triangle Is 55 Meters Find The Length Of Its Sides

Answer 1

ATQ, two sides of a triangle are each 5 meters less than twice the third side of the triangle.

it must be a isosceles triangle since two sides of the triangle are each 5 meters less than twice the third side and hence equal.

let us denote the third side as x

therefore the Length of other two sides is 2x - 5

given perimeter of the triangle = 55 meters

we know that, sum of all sides = perimeter of the triangle

➡ (x) + (2x - 5) + (2x - 5) = 55 meters

➡ x + 2x - 5 + 2x - 5 = 55 meters

➡ 5x - 10 = 55 meters

➡ 5x = 55 + 10

➡ 5x = 65 meters

➡ x = 65/5

➡ x = 13 meters

hence, the sides of the triangle are :-

• third side = x = 13 meters

• length of other two sides = 2x - 5 = (2 × 13) - 5 = 21 meters each

Answer 2

Answer:-

21 m, 21m and 13 m.

Given :-

Perimeter of triangle = 55 m

To find :-

Length of its sides.

Solution :-

Let the side of triangles be AB ,BC and AC respectively.

A/Q.

AB = BC

also,

$AB = BC = 2 AC - 5$

We know that perimeter of triangles of sides AB, BC and AC is given by :-

★ $\boxed{\sf{ P = AB + BC + AC}}$

Now, put the given value

Now, put the given valuewe get,

→$55 = AB + BC + AC$

→$55 = AB + AB + AC$

→$55 = 2 AB + AC$

→$55 = 2(2AC-5) + AC$

→$55 = 4AC -10 + AC$

→$55 +10 = 5AC$

→$65 = 5AC$

→$AC = \dfrac{65}{5}$

→$AC = 13 m$

Now put the value of AC ,

AB = BC = 2 × 13 - 5

= 26 - 5

= 21

Hence,

The sides of triangle are 21 m,21 m and 13 m.

Verification :-

Perimeter of triangle = Sum of its all sides

→ 55 = 21 + 21 + 13

→55 = 55

→ L. H. S = R. H. S verified...