Mathematic Problems

347. példa

Calculate the area of the Isosceles triangle if the base height is 20 cm and the arm height is 24 cm.

a \cdot h_{a} = b \cdot h_{b}

a \cdot 20 = b \cdot 24

b = \frac{a \cdot 20}{24} = \frac{5 \cdot a}{6}

b^{2} = {(\frac{a}{2})}^{2} + h_{b}^{2}

{(\frac{5 a}{6})}^{2} = {(\frac{a}{2})}^{2} + 20^{2}

\frac{25 a^{2}}{36} = \frac{a^{2}}{4} + 400 | \cdot 36

25 a^{2} = 9 a^{2} + 14400

16 a^{2} = 14400

a^{2} = \frac{14400}{16} = 900

a = \sqrt{900} = 30

T = \frac{a \cdot h_{a}}{2} = \frac{30 \cdot 20}{2}

T = 300 c m^{2}

T = 300 c m^{2}

Matematika - Képlettár