Question

*The equal sides of an isosceles triangle are 5 units less than twice the third side. What is the length (in units), of equal sides of the triangle, provided its perimeter is 75 units?*

1️⃣ 35
2️⃣ 25
3️⃣ 29
4️⃣ 41

Answer 1

Let the third side be x

Equal sides= 2x-5

x+2x-5+2x-5 = 75

x+2x+2x-5-5= 75

5x-10= 75

5x= 75+10

5x= 85

x= $\frac{85}{5}$

x = 17

Equal sides = 2x-5 = 2*17 -5

                  = 29 units

So option 3) 29 units is correct.

Answer 2

Length of each equal side is 29 units.

Option 3 is correct.

Given:

• The equal sides of an isosceles triangle are 5 units less than twice the third side.

To find:

• What is the length (in units), of equal sides of the triangle, provided its perimeter is 75 units?

• 1️⃣ 35
• 2️⃣ 25
• 3️⃣ 29
• 4️⃣ 41

Solution:

Concept/Formula to be used:

• Assume unequal side(third side).
• Write two equal sides according to the question.
• Perimeter of triangle= Sum of sides of triangle.

Step 1:

Assume the sides.

Let the third side(or base ) of isosceles triangle is x units .

Equal sides are : (2x-5) units

Step 2:

Find value of x.

As, perimeter is 75 units.

$x + 2x - 5 + 2x - 5 = 75$

or

$5x - 10 = 75$

or

$5x = 85$

or

$x = \frac{85}{5}$

or

$\bf x = 17$

Step 3:

Find the equal sides.

Each equal side is: 2x-5

Put value of x.

Each equal side is: $= (2 \times 17) - 5$

or

$= 34 - 5$

or

Each equal side is $= 29 \:$ unit

Thus,

Length of each equal side is 29 units.

Option 3 is correct.

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