Question

The perimeter of an isosceles triangle is 42 cm its base is 2/3 times the sum of the equal sides find the length of each side and area of triangle.

Answer 1

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Answer 2

The length of each side and area of triangle is 12.6 cm and 78.89 cm²

Given - Perimeter

Find - Length of each side and area of triangle

Solution - Perimeter of triangle = sum of all the sides of triangle

Let the equal sides of triangle be x cm each. Forming the equation -

x + x + (2/3×2x) = 42

2x + 4x/3 = 42

Taking LCM on Left Hand Side, we get 3.

((2x×3) + 4x)/(3) = 42

Shifting 3 on Right Hand Side

6x + 4x = 42×3

10x = 126

$x = \frac{126}{10}$

Performing division

x = 12.6

The length of equal side of triangle = 12.6 cm

Base = (4/3)×12.6

Base = 16.8 cm

Taking base for calculation

Base = 16.8÷2

Base = 8.4 cm

Finding height using Pythagoras theorem

H² = B² + P²

P² = 12.6² - 8.4²

P² = 158.76 - 70.56

P² = 88.2

P = ✓88.2

P = 9.4 cm

Area = 1/2×base×height

Area = 1/2×16.8×9.4

Area = 78.89 cm²

Hence, the length of each side is 12.6 cm and area is 78.89 cm²

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