Question

area of an isosceles triangle is 60 CM square and the length of each one of its equal sides is 13 cm find its base​

Answer 1

Answer:

BC=10,24

Step-by-step explanation:

Please check the attach image

Answer 2

Given:-

• Area of an Isosceles triangle = 60cm²
• Equal sides of an isosceles triangle = 13cm.

To find:-

• Find the length of the base..?

Solutions:-

• Let the length of the base 'a' cm
• Let the length of the height 'h' cm

In ∆ABD,

Area of triangle = 1/2 × 2a × h

=> 60 = 1/2 × 2a × h

=> 60 × 2 = 2a × h

=> 120 = 2ah ...........(i).

By Pythagoras theorem.

=> (AB)² = (BD)² + (AD)²

=> 13² = a² + h²

=> 169 = a² + h² .........(ii).

Adding Eq (i). and (ii), We get.

=> 120 + 169 = 2ah + a² + h²

=> 289 = (a + h)²

=> √289 = a + h

=> 17 = a + h

=> h = 17 - a .........(iii).

Putting the value of h in Eq (i).

=> 120 = 2ah

=> 120 = 2 × a × (17 - a)

=> 120/2 = a(17 - a)

=> 60 = 17a - a²

=> a² - 12a - 5a + 60 = 0

=> a(a - 12) - 5(a - 12) = 0

=> (a - 5) (a - 12) = 0

=> a = 5 or a = 12

So, base => 2a = 2 × 5 = 10cm

Or

base => 2a = 2 × 12 = 24cm

Hence, the base of an isosceles triangle is 10cm and 24cm..