Question

each of the equal sides of an isosceles triangle exceeds its height by 3 CM if the length of the base of the triangle is 18 centimetre find its area and perimeter​

Answer 1

Answer:

Given: base is 18cm

Let the height be x and side be (x+3).

Therefore, perimeter = 18 + (x+3) + (x+3).

perimeter (P) = 24+2x. . . . . . . . . . . . . . . . .(1)

Now, Area(A) = 1/2 × base × height.

1/2 × 18 × x = 9x. . . . . . . . . . . . . . . .(2)

Then, by Pythagoras theorem:

(x+3)² = x² + 9²

x² + 3² + 6x = x² + 81

9 + 6x = 81 - 9.

x = 72/6

x = 12.

sides = (x + 3).

putting the value of x in equation (1)

Perimeter = 18 + 2x.

24 + 2x = 23 + 2 × 12

= 48cm.

Now, putting the value of x in equation (2)

Area = 1/2 × base × height.

Area = 1/2 × 18 × 12

A = 108 cm²

Therefore, area is 108 cm² and perimeter is 48 cm.